# Ppt on congruent triangles

##### Lesson 5.1 Congruence and Triangles. Lesson 5.1 Objectives Identify congruent figures and their corresponding parts. Prove two triangles are congruent.

Surveying  MNP   MKL Given Segment NM  Segment KM –Definition of a midpoint  LMK   PMN –Vertical Angles Theorem  KLM   NPM –ASA Congruence Segment LK  Segment PN –Corresponding Parts of Congruent Triangles Lesson 5.3 Similar Triangles Ratio If a and b are two quantities measured in the same units, then the ratio of a to b is a/b.a/b. It can also/

##### Triangles : a three-sided polygon Polygon: a closed figure in a plane that is made of segments, called sides, that intersect only at their endpoints,

obtuse angle in a triangle. Congruent triangles are triangles that are the same size and shape. Congruent triangles have the corresponding six parts (three angles, three sides) congruent. Definition: Two triangles are congruent if and only if their corresponding parts are congruent. Congruence of triangles is reflexive, symmetric, and transitive. Proving Triangles Congruent SSS: If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Given  STU with/

##### Congruent Triangles. Polygons MNOL and ZYXW are congruent ∆ABC and ∆DEF are congruent Rectangles ABCD and EFGH are not congruent ∆ZXY and ∆JLP are not.

). And no screaming! What did you learn today? What are the five ways (one for right triangles) to prove triangles are congruent? So what do we know about the parts of congruent triangles? Congruent Parts of Congruent Triangles are Congruent Hence, *Remember, you can only use CPCTC, AFTER you have proven two triangles to be congruent! CPCTC Song (sung to the tune of “YMCA” by the Village People) Author of lyrics/

#####  § 5.1 Classifying Triangles Classifying TrianglesClassifying Triangles  § 5.4 Congruent Triangles Congruent TrianglesCongruent Triangles  § 5.3 Geometry.

 B DD  C EE AB  FD BC  DE AC  FE These relationships help define the congruent triangles. Definition of Congruent Triangles If the _________________ of two triangles are congruent, then the two triangles are congruent. corresponding parts If two triangles are _________, then the corresponding parts of the two triangles are congruent. congruent ΔRST  ΔXYZ. Find the value of n. T S R Z X Y 40° (2n + 10)° 50/

##### Congruent Triangles. Polygons MNOL and ZYXW are congruent ∆ABC and ∆DEF are congruent Rectangles ABCD and EFGH are not congruent ∆ZXY and ∆JLP are not.

2 column proof: Given: óBAE óEDB, óABE óDEB Prove: óABE óDEB StatementsReasons So what do we know about the parts of congruent triangles? Corresponding Parts of Congruent Triangles are Congruent Hence, *Remember, you can only use CPCTC, AFTER you have proven two triangles to be congruent! Write a Proof Statement 1.FJ  GH  JFH   GHF 2.HF  FH 3.  JFH   GHF 4.FG  JH Reasons 1.Given/

##### Holt McDougal Geometry 4-4 Congruent Triangles 4-4 Congruent Triangles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz.

Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry 4-4 Congruent Triangles Use properties of congruent triangles. Prove triangles congruent by using the definition of congruence. Objectives Holt McDougal Geometry 4-4 Congruent Triangles corresponding angles corresponding sides congruent polygons Vocabulary Holt McDougal Geometry 4-4 Congruent Triangles Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are/

##### Holt McDougal Geometry 4-4 Congruent Triangles 4-4 Congruent Triangles Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz.

the same length. Holt McDougal Geometry 4-4 Congruent Triangles Use properties of congruent triangles. Prove triangles congruent by using the definition of congruence. Objectives Holt McDougal Geometry 4-4 Congruent Triangles Geometric figures are congruent if they are the same size and shape. / off the use Step 4: Get to the end goal, the PROVE Holt McDougal Geometry 4-4 Congruent Triangles Example 3: Proving Triangles Congruent Given: YWX and YWZ are right angles. YW bisects XYZ. W is the midpoint of /

##### Triangle Midsegment A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle In the figure D is the midpoint of AB.

match up their vertices so that all pairs of CORRESPONDING ANGLES and all pairs of CORRESPONDING SIDES are CONGRUENT. Congruent Polygons Triangle ABC and Triangle PQR are congruent Triangles Congruent Polygons Use the figures to complete each statement. PQ  ____  C  ____ ABC  ______/D A E Jim Smith JCHS Sections 4-2, 4-3, 4-5 When we talk about congruent triangles, we mean everything about them Is congruent. All 3 pairs of corresponding angles are equal…. And all 3 pairs of corresponding sides are equal/

##### Chapter 8 Geometry Part 1. 1.Introduction 2.Classifying Angles 3.Angle Relationships 4.Classifying Triangles 5.Calculating Missing Angles Day…..

to 180 o. Acute Triangles, are triangles that have three acute angle. Examples: Obtuse Triangles, are triangles that have one obtuse angle. Examples: Right Triangles, are triangles that have one right angle. Examples: Scalene Triangles, are triangles that have no congruent sides or angles. Examples: Isosceles Triangles, are triangles with at least two congruent sides and two congruent angles. Examples: Equilateral Triangles, are triangles with three congruent sides and three congruent angles. Examples: More/

##### Objectives: To recognize congruent figures and their corresponding parts.

-> Side-Angle-Side (SAS) Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. A B C D E F Triangle ABC congruent to triangle DEF Example using SAS Given: AB congruent BEBC congruent BD Prove: Triangle ABC congruent triangle DBE A B E C D Homework #20 Due Monday (Oct 22) Page 208/

##### 5.3 Proving Triangles are Congruent – ASA & AAS Objectives: Show triangles are congruent using ASA and AAS.

AAS use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent. Remember! Review Example 10: Using CPCTC A and B are on the edges of a ravine. What is AB? One angle pair is congruent, because they are vertical angles. Two pairs of sides are congruent, because their lengths are equal. Therefore the two triangles are congruent by SAS. By CPCTC, the third/

##### PROPERTIES OF PLANE FIGURES ANGLES & TRIANGLES. Angles Angles are formed by the intersection of 2 lines, 2 rays, or 2 line segments. The point at which.

of supplementary angles. You Try: Find the Measure of the Unknown Angles 1 2 3 Triangle Congruence Congruent triangles are exactly the same size (same side lengths and angle measures) Corresponding sides are the congruent sides of congruent triangles Corresponding angles are the congruent angles of congruent triangles Examples of Congruent Triangles Note: We must name the congruent triangles correctly according to the corresponding angles! You Try: Write a Statement Indicating the Pairs/

##### Triangle Congruence by ASA and AAS

CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent because by definition, corresponding parts of congruent triangles are congruent. 4-4 Prove Triangles Congruent The Basic Idea: Given Information SSS SAS ASA AAS Prove Triangles Congruent Show CorrespondingParts Congruent CPCTC Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 SSS, SAS, ASA, AAS, (and/

##### Proving Triangles are Congruent SSS, SAS; ASA; AAS

AND SAS CONGRUENCE POSTULATES If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Sides are congruent Angles are congruent Triangles are congruent If and then  ABC  DEF 1. AB DE 4. A D 2. /postulate SSS  postulate Not Enough Info SAS  postulate SAS  postulate Use the SSS Congruence Postulate to show that  NMP   DEF. Congruent Triangles in a Coordinate Plane Use the SSS Congruence Postulate to show that  NMP   DEF. SOLUTION MN = 4 and DE = 4 /

##### §3.1 Triangles The student will learn about: congruent triangles,

BC  EF AC  DF Order in the statement, Δ ABC  Δ DEF, is important. 8 We Will Use CPCTE To Establish Three Types of Conclusions 1. Proving triangles congruent, like Δ ABC and Δ DEF. 2. Proving corresponding parts of congruent triangles congruent, like Establishing a further relationship, like A  B. 9 Some Postulate Postulate 12. The SAS Postulate Every SAS correspondence is a congruency. Postulate 13. The ASA/

##### 2.3: Exploring Congruent Triangles

–4 Applies the concepts of congruency by solving problems on or off a coordinate plane; or solves problems using congruency involving problems within mathematics or across disciplines or contexts. Definitions Congruent triangles: Triangles that are the same size and the same shape. A B C D E F In the figure DEF  ABC Congruence Statement: tells us the order in which the sides/

##### 4-4 Congruent Triangles Warm Up Lesson Presentation Lesson Quiz

values for mBCA and mBCD. (2x – 16)° = 90° 2x = 106 Add 16 to both sides. x = 53 Divide both sides by 2. Example 2B: Using Corresponding Parts of Congruent Triangles Given: ∆ABC  ∆DBC. Find mDBC. ∆ Sum Thm. mABC + mBCA + mA = 180° Substitute values for mBCA and mA. mABC + 90 + 49.3 = 180 m/

##### Congruent Triangles Geometry Chapter 4.

B E C F If ABC,DEF Right s, AB  DE, AC  DF, then ABC  DEF. 4.5 Using Congruent Triangles Definition of Congruent Triangles (rewritten) Corresponding Parts of Congruent Triangles are Congruent CPCTC is used often in proofs involving congruent triangles. A is the midpoint of MT. A is the midpoint of SR. MS ll TR 1. 1. Given UR ll ST R and T are right angles/

##### Chapter 10 Congruent and Similar Triangles Introduction Recognizing and using congruent and similar shapes can make calculations and design work easier.

named in order. THE ANGLE MEASURES OF A TRIANGLE AND CONGRUENT TRIANGLES The sum of the angle measures of a triangle is 180 o Example 30 o 65 o ? ? = 85 o Congruent triangles 90 o 60 o 5 cm ? ? Example Congruent triangles are triangles with the same shape and size Angle = 60 o ; side = 5cm Isosceles triangles An isosceles triangle is the triangle which has at least two sides with the same/

##### CHAPTER 4 Congruent Triangles SECTION 4-1 Congruent Figures.

two sides THEOREM 4-4 If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. (HL) Ways to Prove Two Triangles Congruent All triangles – SSS, SAS, ASA, AAS Right Triangle - HL SECTION 4-6 Using More than One Pair of Congruent Triangles SECTION 4-7 Medians, Altitudes, and Perpendicular Bisectors Median – is the segment with endpoints/

##### Session 6 Daily Check 1) and are midsegments of the triangle. Find the length of RT and UW. (2 points each) 2) Use the Triangle Proportionality Theorem.

: MCC9-12.G.SRT5, CO.7-8 Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Congruent triangles have congruent sides and congruent angles. The parts of congruent triangles that “match” are called corresponding parts. Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Complete each congruence statement. CA E D B F DEF/

##### Congruent Triangles Today’s Learning Goals We will determine three different ways to know if two triangles are identical. We will begin to see identical.

same. They are just rotated or flipped in different ways. So, if all three sides of two triangles are the same, then the two triangles are congruent. This property is known as SSS (side-side-side). Congruent Triangles Consider the following two pairs of triangles. Which pair has two congruent triangles? Explain how you know. 6 8 13 6 9 14 4 9 11 4 9 A BC/

##### Warm-Up Exercises Tell whether it is possible to draw each triangle.

properties below will be useful in such proofs. THEOREM A B C Theorem Properties of Congruent Triangles Reflexive Property of Congruent Triangles Every triangle is congruent to itself. D E F Symmetric Property of Congruent Triangles If  , then  . ABC DEF J K L Transitive Property of Congruent Triangles If  and  , then  . JKL ABC DEF Goal 2 Classwork: p. 205 #1-9 Assignment: pp. 206-9 #11-29 odd, 30-33/

##### 3.7 Midsegments of Triangles

included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent. Triangle Congruences ASA (Angle-Side-Angle) Postulate If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent. Practice In each pair below, the triangles are congruent. Tell which triangle congruence postulate allows you/

##### Chapter 4 Congruent Triangles.

-26 Page 254 #6-9, 16-19, 37-40 4. 6: Congruence in Right Triangles 4 4.6: Congruence in Right Triangles 4.7: Congruence in Overlapping Triangles Students will be able to Prove right triangles are congruent using the Hypotenuse Leg Theorem Identify congruent overlapping triangles and use congruent triangle theorems to prove triangles are congruent. MA.912.G.4.4 andMA.912.G.4.5 and MA.912.G/

##### Triangle Congruence Theorems

Theorems Geometry Triangle Congruence Theorems Congruent Triangles Congruent triangles have three congruent sides and and three congruent angles. However, triangles can be proved congruent without showing 3 pairs of congruent sides and angles. The Triangle Congruence Postulates &Theorems AAS ASA SAS SSS FOR ALL TRIANGLES LA HA LL HL FOR RIGHT TRIANGLES ONLY Theorem If two angles in one triangle are congruent to two angles in another triangle, the third angles must also be congruent. Think about/

##### Lesson: Pages: Objectives: 4.3 Exploring CONGRUENT Triangles 196 – 197  To NAME and LABEL Corresponding PARTS of CONGRUENT Triangles  To STATE the CPCTC.

Size SAME Shape GEOMETRY 4.3 Congruent Polygons have the: SAME Size SAME Shape Congruent TRIANGLES have Congruent CORRESPONDING SIDES Congruent CORRESPONDING Angles GEOMETRY 4.3 Congruent TRIANGLES have Congruent CORRESPONDING SIDES Congruent CORRESPONDING Angles A B C DE F GEOMETRY 4.3 Congruent TRIANGLES have Congruent CORRESPONDING SIDES Congruent CORRESPONDING Angles A B C DE F GEOMETRY 4.3 Congruent TRIANGLES have Congruent CORRESPONDING SIDES Congruent CORRESPONDING Angles Because CORRESPONDING parts/

##### 2.3: Exploring Congruent Triangles M(G&M)–10–4 Applies the concepts of congruency by solving problems on or off a coordinate plane; or solves problems.

E D then the 2 triangles are CONGRUENT! ***** only used with right triangles**** The Triangle Congruence Postulates &Theorems LA HALL FOR RIGHT TRIANGLES ONLYFOR ALL TRIANGLES Only this one is new Summary Any Triangle may be proved congruent by: (SSS) (SAS) (ASA) (AAS) Right Triangles may also be proven congruent by HL ( Hypotenuse Leg) Parts of triangles may be shown to be congruent by Congruent Parts of Congruent Triangles are Congruent (CPCTC). Example 1 F E/

##### Chapter 4 Notes. 4.1 – Triangles and Angles A Triangle  Three segments joining three noncollinear points. Each point is a VERTEX of the triangle. Segments.

shapes sharing a side, you state that fact using the reflexive property of congruence! A C B D Draw and write down if the triangles are congruent, and by what thrmpost Proofs! The way I like to think about it to look at all the angles and sides, and don’t/B A D E C B A D E 4.5 – Using Congruent Triangles A B C D E Some Ideas that may help you. If they want you to prove something, and you see triangles in the picture, proving triangles to be congruent may be helpful. If they want parallel lines, look to use /

##### 5.1 Angle Relationships in a Triangle Triangles can be classified by the measure of their angles. These classifications include, obtuse triangles, right.

states if two angles of one triangle are congruent to two angles of another triangle and two corresponding non-included sides are congruent, then the triangles are congruent. The Angle-Angle-Side Congruence Theorem states if two angles of one triangle are congruent to two angles of another triangle and two corresponding non-included sides are congruent, then the triangles are congruent. Lesson 5.7 Proving Triangles Congruent: HL The Hypotenuse-Leg Congruence Theorem/

##### Angle Relationships in Triangles Holt Geometry Lesson Presentation Lesson Presentation Holt McDougal Geometry.

Presentation Holt McDougal Geometry CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent. SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent. Remember! Example: Engineering Application A and B are on the edges of a/

##### Exploring Congruent Triangles. Congruent triangles: Triangles that are the same size and shape – Each triangle has six parts, three angles and three sides.

sides – If the corresponding six parts of one triangle are congruent to the six parts of another triangle, then the triangles are congruent This is abbreviated by CPCTC (corresponding parts of congruent triangles are congruent) – Orientation of the triangles is not important. This means that the triangles can be flipped, slid and turned around, and if the corresponding parts are congruent, the triangles are congruent Segments: Angles: 1. 2. 3. Note: The order/

##### Properties of Congruent Triangles. Figures having the same shape and size are called congruent figures. Are the following pairs of figures the same? Congruence.

For example,  U =  F, TV = ED  V =  D, △ TUV  △ EFD (AAS) 130° Follow-up question 3 In each of the following, name a pair of congruent triangles and give the reason. (a) A B C E F G 45° 40° 45° 5.25 cm △ ABC  △ FEG (ASA) ◄ ∠ B = ∠ E, BC = EG, ∠ / corresponding sides are proportional. (i)All their corresponding angles are equal, ~is similar to △XYZ△XYZ △ABC△ABC Note: The corresponding vertices of congruent triangles should be written in the same order. If △ ABC ~ △ XYZ... 4 cm A B C 4.5 cm 40° X Y Z 2/

##### Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Warm Up 9/29/08 1.Give the restrictions on the third.

the properties and characteristics of polygons? Standard: MM1G1.e. Today’s Question: What does it mean for two triangles to be congruent? Standard: MM1G.3.c. Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Congruent triangles have congruent sides and congruent angles. The parts of congruent triangles that “match” are called corresponding parts. Essential Question: What does it mean for two/

##### Math 2 Geometry Based on Elementary Geometry, 3 rd ed, by Alexander & Koeberlein 3.1 Congruent Triangles.

Alexander & Koeberlein 3.1 Congruent Triangles Definition Two triangles are congruent when the six parts of the first triangle are congruent to the six parts of the second triangle. Definition Two triangles are congruent when the six parts of the first triangle are congruent to the six parts of the second triangle. What are the six parts? Definition Two triangles are congruent when the six parts of the first triangle are congruent to the six parts/

##### Learning Goal:  IWBAT to determine whether two triangles are congruent by using the triangle congruence postulates and theorem. Homework :  HW 3.5: Triangle.

made with two straws and a 45° angle between them?  If you know that two sides of a triangle are congruent to two sides of another triangle, what other information do you need to tell whether the triangles are congruent? Congruence Postulates  Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, tell which congruence postulate you would use/

##### CHAPTER 4 Congruent Triangles. What does CONGRUENCE mean? Congruent angles- have equal measures Congruent segments- have equal lengths.

- have equal lengths What did you notice about these pictures? What does it mean for two objects or figures to be congruent? Congruent figures- have the same shape and size What about congruent triangles? Congruent Triangles (same shape and size) Are these triangles congruent? Can you rotate or reflect them so that they fit on top of one another? What are the corresponding angles? A F E D/

##### Chapter 4 Presentation CONGRUENT TRIANGLES. 4.1 Apply Triangle Sum Properties  A triangle is classified by its angles and sides.  Angles: Right=90°

, HL & SSS & SAS 4.6 Use Congruent Triangles  CPCTC  C: Corresponding  P: Parts of  C: Congruent  T: Triangles are  C: Congruent 4.7 Use Isosceles and Equilateral Triangles  Base Angles Theorem: If 2 sides of a triangle are congruent, the angles opposite them are congruent.  Converse of Base Angles Theorem: If 2 angles of a triangle are congruent, then the sides opposite them are congruent.  Corollary to Base Angles Theorem: If a/

##### Learning Goal:  IWBAT to solve for unknown side lengths and angles in triangles by using theorems about triangles. Homework :  HW 3.8: Midsegment Theorem.

Agenda: 1.Do Now (10 min) 2.H-L Congruence Theorem (10 min) 3.Midsegment Theorem (30 min) 4.Isosceles Triangles (25 min) 5.Congruent Triangles (15 min) 6.Closure (5 min) Retake Quizzes:  10 th and 11 th graders can take retakes for any quiz/with a proof or counterexample.  If two legs of a right triangle are the same length as two legs of another right triangle, then the triangles MUST be congruent. Explore Congruence of Right Triangles  Right triangles consist of two legs, a hypotenuse, and a 90° angle./

##### Angles of a Triangle and Congruent Triangles April 24, 2008.

the same shape and size, they are called congruent. We have already discussed congruent segments (segments with equal lengths) and congruent angles (angles with equal measures). Congruent Triangles Triangles ABC and DEF are congruent. If you mentally slide triangle ABC to the right, you can fit it exactly over triangle DEF by matching up the vertices. Definition of congruent triangles Two triangles are congruent if and only if their vertices can be matched/

##### Proving Triangles are Congruent: SSS, SAS Section 5.2.

Congruent TrianglesTriangles that are the same shape and size are congruent. ▫Each triangle has three sides and three angles. ▫If all 6 parts (3 corresponding sides and 3 corresponding angles) are congruent….then the triangles are congruent. Review CPCTC – Corresponding Parts of Congruent Triangles are Congruent/. line bisector Def. midpoint Reflexive Postulate SSS Postulate R TP X Given: Prove: Example 10: Proving Triangles Congruent Given: BC ║ AD, BC  AD Prove: ∆ABD  ∆CDB ReasonsStatements 5. SAS 5. /

##### CONFIDENTIAL 1 Geometry Triangle Congruence SSS and SAS.

measure of the included angle, you can construct one and only one triangle. CONFIDENTIAL 12 Construction Congruent triangles using SAS STEP1: Use a straightedge to draw two segments and one angle, or copy the given/ Hypothesis Conclusion ∆ABC = ∆DEF Postulate: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. CONFIDENTIAL 26 Using SSS to prove triangle Congruent CONFIDENTIAL 27 An included angle is an angle formed by two adjacent sides/

##### Congruent Triangles Part 2 Unit 4 SOL G.5 & G.6 Sections 4.5, 4.6, 4.7 Review & Proofs Resource: Henrico Geometry.

A 42 Seg. bisector implies segments. Back STATEMENTSREASONS S S … 43 Angle bisector implies angles. Back STATEMENTSREASONS A … 44 implies right ( ) angles. Back STATEMENTSREASONS A … S 4. Given 4. 45 Congruent Triangles Proofs 1. Mark the Given and what it implies. 2. Mark … Reflexive Sides / Vertical Angles 3. Choose a Method. (SSS, SAS, ASA) 4. List the Parts … in the order of/

##### Using Congruent Triangles Section 5.5. Objective Show corresponding parts of congruent triangles are congruent.

Section 5.5 Objective Show corresponding parts of congruent triangles are congruent. Key Vocabulary - Review Corresponding parts Review: Congruence Shortcuts Congruent Triangles (CPCTC) congruent triangles cp ct c Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent. Corresponding sides are congruent Corresponding angles are congruent Example: Name the Congruence Shortcut or CBD SAS ASA SSS SSA CBD Your Turn: Name the Congruence Shortcut/

##### Review: Solving Systems x 2y+3 x+y 12 Find the values of x and y that make the following triangles congruent.

x and y that make the following triangles congruent. Congruent Triangles (CPCTC) congruent triangles cp ctc Two triangles are congruent triangles if and only if the corresponding parts of those congruent triangles are congruent. Corresponding sides are congruent Corresponding angles are congruent Congruence Statement When naming two congruent triangles, order is very important. Third Angle Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also/

##### Congruent Triangles In two congruent figures, all the parts of one figure are congruent to the corresponding parts of the other figure. This means there.

? A coordinate proof involves placing geometric figures in a coordinate plane. Congruent Triangles Which triangles are congruent by the SSS Postulate? Not congruent by SSS Congruent Triangles Are these congruent by SAS? Are these congruent by HL? How about: Not right triangles! Congruent Triangles Are these triangles congruent by ASA? Yes! No Congruent Triangles Are these triangles congruent by AAS? How about now? Yes No Congruent Triangles There are a couple of methods for organizing your thoughts when/

##### Congruence in Right Triangles

. ZW YX by CPCTC if ZWM YXM. Look at MWX. MW MX by the Converse of the Isosceles Triangle Theorem. You can prove these triangles congruent using ASA as follows: Quick Check 4-7 Using Corresponding Parts of Congruent Triangles GEOMETRY LESSON 4-7 Using Two Pairs of Triangles Write a paragraph proof. Given: XW YZ, XWZ and YZW are right angles. Prove: XPW YPZ Plan/

##### 4-2 Some ways to prove triangles Congruent

Reasons E is the midpoint of of MJ Given ME = JE Def. of Midpoint TE JE < MET = < JET TE = ________ MET = JET Proving Triangles Congruent Given: E is the midpoint of MJ; TE MJ Prove: MET = JET M J E Statements Reasons E is the midpoint of of MJ Given ME =/ JE Def. of Midpoint TE JE < MET = < JET TE = ________ MET = JET Proving Triangles Congruent Given: E is the midpoint of MJ; TE MJ Prove: MET = JET M J E Statements Reasons E is the midpoint of of MJ Given ME =/

##### Proving Triangles Congruent

EC by midpoint theorem. Since E is the midpoint of segment BD, segment BE is congruent to segment ED by midpoint theorem. Angle AEB and angle CED are vertical angles by definition. Therefore angle AEB is congruent to angle CED because all vertical angles are congruent. Triangle ABE is congruent to triangle CED by the side-angle-side postulate. 3. AEB and CED are vertical angles/

##### 4.3 Congruent Triangles We will…

4.3 Congruent Triangles We will… …name and label corresponding parts of congruent triangles. …identify congruence transformations. Corresponding parts of congruent triangles Triangles that are the same size and shape are congruent triangles. Each triangle has three angles and three sides. If all six corresponding parts are congruent, then the triangles are congruent. Corresponding parts of congruent triangles X Z Y A C B If ΔABC is congruent to ΔXYZ , then vertices of the two triangles correspond in/