Breakthrough Math 9 Name: ________________________

Day 13 Guided Notes Date: _________________________

Proving Triangle Congruence and CPCTC

Objective: Today, you will be able to match

congruent triangles and prove congruency Proving Behavior: by writing the congruent

sides and angles of congruent triangles and writing

out proofs

Purpose: We are doing this because knowing which parts of congruent triangles match help with

writing proofs

Do Now

1. Below are two different versions of triangles HYZ and HIJ. (Assume scale is not

consistent). Determine which pair of triangles is similar, then justify your using a

similarity property (SSS, SAS, AA).

2. Write one way that Sam and Grace can improve as your teachers for the rest of the

summer:

Lesson

Congruence - Two polygons are ____________ if and only if their parts are congruent. Thus we

know that triangles are congruent if their corresponding sides and angles are congruent.

Congruence is denoted by this symbol:

Q: Are two congruent triangles always similar? Are two similar triangles always congruent?

______________________________________________________________________________

Determining Corresponding Parts – Determining corresponding parts of triangles requires

careful attention to how the triangles are named.

1. Corresponding points are determined by the order in which the points are listed in triangle

names.

Suppose ΔABC is congruent to ΔRST. Then the corresponding points are A and R, B and S, and

C and T.

Do: Draw a picture of the two congruent triangles.

2. The angle denoted by each point is congruent to the angle denoted by the corresponding point

in the other triangle. So A R

Do: Write the other two corresponding angle pairs:

3. The side denoted by two points is congruent to the side denoted by the corresponding points in

the other triangle. So AB RS

Do: Write the other two corresponding side pairs:

Terms And Tools for Proof Writing

Step 4: Bisect – A line segment bisects an angle if it divides it into two equal parts. A line

segment can also bisect another line segment if the intersection between the two line segments is

the midpoint of the second line segment.

CPCTC - Congruence Parts of Congruent Triangles are Congruent

Congruence Postulates

Angle-Side-Angle Postulate – If two _____ and the included ____ of one triangle are congruent

to two angles and the included side of another triangle, then the triangles are congruent.

Angle-Angle-Side Postulate - If two angles and a non-included side of one triangle are

__________ to two angles and a non-included side of another triangle, then the two triangles are

__________.

Structured Practice

3.

PROOF Write a two-column proof for each of the following questions.

Guided Practice

PROOF Write a two-column proof for each of the following questions.

Guided Practice

Independent Practice

6.

7.

PROOF Write a two-column proof for reach of the questions

8.