4-3 Congruent Triangles - Weebly

4-3 Congruent Triangles

Warm Up 1. Name all sides and angles of FGH.

2. What is true about K and L? Why?

LEARNING GOALS ? LESSON 4.3 4.3.1: Use properties of congruent triangles. 4.3.2: Prove triangles congruent by using the definition of congruence.

__________________ ___________ and __________ are in the same _____________ in polygons with an equal number of sides. Two polygons are ______________ if and only if their corresponding sides are congruent.

In a congruence statement, the ____________ of the vertices indicates the corresponding parts.

Given that polygon MNOP polygon QRST, identify the congruent corresponding part.

1. NO ____

2. T ____

4-3 Congruent Triangles

Example 1A: Naming Congruent Corresponding Parts Given: PQR STW, identify all pairs of corresponding congruent parts.

Example 1B: Using Corresponding Parts of Congruent Triangles a. Given: ABC DBC.

Find the value of x.

b. Given: ABC DBC. Find mDBC.

c. Given: ABC DEF Find the value of x.

d. Given: ABC DEF Find mF.

4-3 Congruent Triangles

Example 2: Proving Triangles Congruent Given: YWX and YWZ are right angles. YW bisects XYZ. W is the midpoint of XZ. XY YZ. Prove: XYW ZYW

Statements 1. YWX and YWZ are rt. s. 2. YW bisects XYZ. 3. W is the midpoint of XZ. XY YZ.

Reasons 1. Given 2. Given 3. Given

___. XYW ZYW

Given: PR and QT bisect each other. PQS RTS, QP RT Prove: QPS TRS

Statements 1. QP RT, PQS RTS 2. PR and QT bisect each other.

Reasons

1. Given 2. Given

4-3 Congruent Triangles

Given: C is the midpoint of BD and AE. A E, AB ED Prove: ABC EDC

Statements

1. A E 2. C is mdpt. of BD and AE 3. AB ED

Reasons

1. Given 2. Given 3. Given

7. ABC EDC

Given: AD bisects BE. BE bisects AD. AB DE,

Prove: ABC DEC

A D

Statements 1. A D 2. BE bisects AD.

Reasons 1. Given 2. Given

7. ABC DEC

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