CONGRUENT TRIANGLES. Congruence We know… Two SEGMENTS are congruent if they’re the same length. Two ANGLES are congruent if they have the same measure.

Slides:

Advertisements

Similar presentations

Concept: Use Similar Polygons

Advertisements

4-4 Using Congruent Triangles: CPCTC

4-2 Triangle Congruence by SSS and SAS

Hypotenuse – Leg Congruence Theorem: HL

Warm-up: List the 6 pairs of corresponding parts which are congruent:

Congruent Polygons. Congruent segments have the same length.

Test For Congruent Triangles. Test 1 3 cm 4 cm 3 cm Given three sides : SSS Two triangles are congruent if the three sides of one triangle are equal to.

Congruent Triangles.  Standard 25: Identify interior and exterior angles of a triangle and identify the relationships between them.  Standard 26: Utilize.

4-2: Triangle Congruence by SSS and SAS 4-3: Triangle Congruence by ASA and AAS 4-4: Using Corresponding Parts of Congruent Triangles.

5-7 Inequalities in Two Triangles

7-3 Proving Triangles Similar

Thursday, January 10, 2013 A B C D H Y P E. Homework Check.

Do Now #28:. 5.4 Hypotenuse-Leg (HL) Congruence Theorem Objective: To use the HL Congruence Theorem and summarize congruence postulates and theorems.

Angle – Angle Similarity, Day 2. Warm Up In an isosceles triangle, the two equal sides are called legs and the third side is called the base. The angle.

Notes Over Congruence When two polygons are ___________their corresponding parts have the _____ _______. congruent same measure 1. Name the corresponding.

DO NOW!!! Solve for “x”..

Section 4.2 Congruence and Triangles. Two figures are congruent if they have exactly the same size and shape.

Geometry Sections 6.4 and 6.5 Prove Triangles Similar by AA Prove Triangles Similar by SSS and SAS.

7.5 Proportions and Similar Triangles

8-3 Proving Triangles Similar M11.C B

Congruent Polygons Sec 6.5 GOALS: To identify congruent polygons.

SIMILARITY: A REVIEW A REVIEW Moody Mathematics. Midsegment: a segment that joins the midpoints of 2 sides of a triangle? Moody Mathematics.

Triangle Congruence. 3 line segments (dried spaghetti sticks – make three different sizes) Take 3 line segments Make a triangle Mark the vertices Draw.

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.

Drill Write your homework in your planner Take out your homework Find all angle measures:

The distance from any point on a circle to the center is a constant called the radius. The length of any line segment from a point on a circle to the.

Warm Up  For both right triangles, find the value of x. x x

CHAPTER 4 SECTION 2 Triangle Congruence by SSS and SAS.

The product of the means equals the product of the extremes.

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

Triangle Similarity Keystone Geometry. 2 Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding.

Proving Triangles are Congruent: SSS and SAS Sec 4.3

For 9 th /10 th grade Geometry students Use clicker to answer questions.

4.2 Triangle Congruence by SSS and SAS You can prove that two triangles are congruent without having to show that all corresponding parts are congruent.

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

Proving Triangle Congruency. What does it mean for triangles to be congruent? Congruent triangles are identical meaning that their side lengths and angle.

Date: Topic: Proving Triangles Similar (7.6) Warm-up: Find the similarity ratio, x, and y. The triangles are similar. 6 7 The similarity ratio is: Find.

Section Review Triangle Similarity. Similar Triangles Triangles are similar if (1) their corresponding (matching) angles are congruent (equal)

4-1: Congruent Figures.  Congruent Polygons  Have congruent corresponding parts  Must list corresponding vertices in the same order when naming. Congruent.

Chapter 9, Section 5 Congruence. To be congruent: –corresponding parts (sides/ angles) have the same measure.

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

Geometry-Part 7.

4-2 Triangle Congruence by SSS and SAS

Proving Triangles are Congruent

7.4 Showing Triangles are Similar: SSS and SAS

Proving Triangles are Similar

Similarity Postulates

Inequalities in two triangles

Proving Triangles Congruent: SSS and SAS

4-2 Triangle Congruence by SSS and SAS

Proving Triangles Congruent

4.2-Congruence & Triangles

5.3 Proving Triangle Similar

Proving Triangles Similar

7-3 Similar Triangles.

4-2 Some Ways to Prove Triangles Congruent (p. 122)

SSS and, AAS Triangle Congruence Theorems

5.3 Proving Triangle Similar

Proving Triangles Similar.

Congruence and Triangles

4-1 Congruent Figures 4-2 Triangle Congruence by SSS and SAS

Proving Triangles Similar.

Similar Similar means that the corresponding sides are in proportion and the corresponding angles are congruent. (same shape, different size)

Properties of Triangle Congruence

Congruent Triangles Section 4.2.

How can you show that two triangles

Warm Up 1 ( Write a congruence statement

4-1 Congruent Figures 4-2 Triangle Congruence by SSS and SAS

Inequalities in Two Triangles

Module 16: Lesson 4 AA Similarity of Triangles

Presentation transcript:

CONGRUENT TRIANGLES

Congruence We know… Two SEGMENTS are congruent if they’re the same length. Two ANGLES are congruent if they have the same measure. 2” 60 °

Third Angles Theorem If two angles of one triangle are congruent to two angles of a second triangle, then: The third angles are also congruent The two triangles are SIMILAR (but not necessarily CONGRUENT)

Triangle Congruence Congruence: Two triangles are CONGRUENT if (and only if) they have three pairs of congruent sides and three pairs of congruent angles.

Corresponding Parts If two triangles are congruent, then: The corresponding sides are the sides that are congruent The corresponding angles are the angles that are congruent

Minimum Information for Congruence There are three angles and three sides to every triangle, so there are six pieces of information. We need to know that at least THREE pieces of information match (with some restrictions).

Theorem #1: SSS If the side lengths of two triangles are congruent, then the triangles are congruent.

Theorem #2: SAS If two sides and the angle between them are congruent, then the triangles are congruent.