4.4 Proving Congruence – SSS and SAS What you’ll learn: 1.To use SSS Postulate to test for triangle congruence. 2.To use the SAS Postulate to test for.

Slides:

Advertisements

Similar presentations

Proving Triangles Congruent

Advertisements

Proving Triangles Congruent

4.3 to 4.5 Proving Δs are  : SSS, SAS, HL, ASA, & AAS

4-4 Using Congruent Triangles: CPCTC

CCGPS Analytic Geometry

Proving Δs are  : SSS, SAS, HL, ASA, & AAS

1 MM1G3c Proving Triangles Congruent (AAS, HL). 2 Postulates AAS If two angles and a non included side of one triangle are congruent to the corresponding.

Blue – 3/9/2015 Gold – 3/10/2015.  Last 2 classes, we talked about 3 ways we can determine triangle congruence.  CPCTC – All 3 sides and 3 angles of.

Section 4-3 Triangle Congruence (ASA, AAS) SPI 32C: determine congruence or similarity between triangles SPI 32M: justify triangle congruence given a diagram.

Proving Triangles Congruent

4-4 & 4-5: Tests for Congruent Triangles

Proving Triangles Congruent Advanced Geometry Triangle Congruence Lesson 2.

Proving Triangles Congruent

2.11 – SSS, SAS, SSA.

4.1 Detours & Midpoints Obj: Use detours in proofs Apply the midpoint formulas Apply the midpoint formulas.

Bellwork….. The given figure is a parallelogram. Solve for the missing variable (4c + 5)º (2c +19)° Hint: Alternate interior angles of parallel line cut.

4.3 Proving Triangles are Congruent Side-Side-SideSide-Angle-Side.

& 5.2: Proving Triangles Congruent

Proving Congruence: SSS and SAS

4.3 – Prove Triangles Congruent by SSS

Proving Triangles Congruent. Steps for Proving Triangles Congruent 1.Mark the Given. 2.Mark … reflexive sides, vertical angles, alternate interior angles,

Theorems Theorem 6.6: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. ABCD is a parallelogram.

Warm-Up! Find the Distance and Midpoint between the two points (-12, 6) and (-4, -3)

(4.4) CPCTC Corresponding Parts of Congruent Triangles Congruent

4.4 - Prove Triangles Congruent by SAS and HL. Included Angle: Angle in-between two congruent sides.

6.3 Proving Quadrilaterals are Parallelograms

4-2 Triangle Congruence by SSS and SAS. Side-Side-Side (SSS) Postulate If the three sides of one triangle are congruent to the three sides of another.

Unit 2 Part 4 Proving Triangles Congruent. Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles.

Angle Relationship Proofs. Linear Pair Postulate  Angles which form linear pairs are supplementary.

1Geometry Lesson: Pairs of Triangles in Proofs Aim: How do we use two pairs of congruent triangles in proofs? Do Now: A D R L B P K M.

4-4 Proving Congruence- SSS, SAS. Congruent Means that corresponding parts are congruent, Matching sides and angles will be congruent.

Angle-Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Proving Congruence – SSS, SAS Side-Side-Side Congruence Postulate (SSS) If the sides of one triangle are congruent to the sides of a second triangle, then.

Proving Triangles are Congruent: SSS and SAS Sec 4.3

Proving Congruence SSS, SAS Postulate 4.1 Side-Side-Side Congruence If the sides of one triangle are congruent to the sides of a second triangle, then.

6.3 Proving Quadrilaterals are Parallelograms Standard: 7.0 & 17.0.

Unit 7 Congruency and Similarity Proving Triangles Congruent (SSS, SAS, ASA, AAS, and HL)

Triangle Congruence by SSS & SAS Objective: To Determine whether triangles are congruent using SSS and SAS postulate.

Warm Up: Tell whether it is possible to draw each triangle. 1.Acute scalene triangle 2.Obtuse equilateral triangle 3.Right isosceles triangle 4.Scalene.

Using Special Quadrilaterals

6.2 Proving Quadrilaterals are Parallelograms. Theorems If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a.

 Students will apply the SSS & SAS Similarity Theorems to determine similarity in triangles.  Why? So you can show that triangles are similar, as seen.

4-4 Using Corresponding Parts of Congruent Triangles I can determine whether corresponding parts of triangles are congruent. I can write a two column proof.

Warm Up Check homework answers with each other!. Ch : Congruence and Triangles Students will prove triangles congruent using SSS, SAS, ASA, AAS,

Triangle Proofs. USING SSS, SAS, AAS, HL, & ASA TO PROVE TRIANGLES ARE CONGRUENT STEPS YOU SHOULD FOLLOW IN PROOFS: 1. Using the information given, ______________.

Chapters 2 – 4 Proofs practice. Chapter 2 Proofs Practice Commonly used properties, definitions, and postulates  Transitive property  Substitution property.

5.6 Proving Quadrilaterals are Parallelograms. Objectives: Prove that a quadrilateral is a parallelogram.

Proving Δs are  : SSS, SAS, HL, ASA, & AAS

Proving Triangles are Congruent

Using Triangle Congruence to Prove Sides and Angles Congruent C h. 5-2

Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent?

4.5 Proving Congruence – ASA and AAS

Proving Triangles Congruent

Proving Triangles Congruent: SSS and SAS

4.3 – Prove Triangles Congruent by SSS

Three ways to prove triangles congruent.

4.3 and 4.4 Proving Δs are  : SSS and SAS AAS and ASA

Aim: Do Now: ( ) A B C D E Ans: S.A.S. Postulate Ans: Ans:

Class Greeting.

Warm-Up Find the value of x: 30° 40° x° x° 35° 25° 74° 44° x°

Proving Triangles Congruent

8.3 Methods of Proving Triangles Similar

Warm-Up #38 Line M goes through the points (7, -1) and (-2, 3). Write an equation for a line perpendicular to M and through the origin. What are the new.

9.2 Proving Quadrilaterals are Parallelograms

Ex: Given: Prove: CPCTC:

4-2 Triangle congruence by sss & sas

Presentation transcript:

4.4 Proving Congruence – SSS and SAS What you’ll learn: 1.To use SSS Postulate to test for triangle congruence. 2.To use the SAS Postulate to test for triangle congruence.

More ways to prove 2 triangles are  : Postulate 4.1 SSS Congruence If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Postulate 4.2 SAS Congruence If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Determine whether  ABC  DEF. Explain. A(-6,1), B(1,2), C(-1,-4), D(0,5), E(7,6), F(5,0)

Assumables The following can be assumed from the given picture: 1.Vertical angles are congruent. (reason: vert.  congruent) 2.A segment or angle shared by both triangles is congruent to itself. (reason: reflexive)

Given: RQ  TS, RQ  TS Prove:  QRT  STR 1.RQ  TS, RQ  TS 2.  QRT  RTS 3.RT  RT 4.  QRT  STR 1.Given 2.Alt. int. angles  3.Reflexive 4.SAS RS T Q

Determine which postulate can be used to prove that the triangles are congruent. Write “not possible” if no theorem applies. 1. Yes, SSS 2. Not possible 3. Yes, SAS

How to use CPCTC When you are asked to prove that corresponding parts (angles or sides) of 2 triangles are congruent, you may have to prove the 2 triangles are congruent first. Then by CPCTC, the corresponding parts are also congruent. Ex: Given:  B  D, AB  AD, BC  CD. Prove:  BAC  DAC StatementsReasons  B  D, AB  AD, BC  CD given  CBA  CDASAS  BAC  DACCPCTC A B C D

Homework p even