Identify Corresponding Congruent Parts

Show that polygons ABCDE and RTPSQ are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.

Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ.

Sides:

Angles:

A. A

B. B

C. C

D. D

The support beams on the fence form congruent triangles. In the figure ΔABC ΔDEF, which of the following congruence statements directly matches corresponding angles or sides?

A.

B.

C.

D.

Use Corresponding Parts of Congruent Triangles

O P CPCTC

mO = mP Definition of congruence

6y – 14 = 40 Substitution

In the diagram, ΔITP ΔNGO. Find the values of x and y.

Use Corresponding Parts of Congruent Triangles

6y = 54 Add 14 to each side.

y = 9 Divide each side by 6.

NG = IT Definition of congruence

x – 2y = 7.5 Substitution

x – 2(9) = 7.5 y = 9

x – 18 = 7.5 Simplify.

x = 25.5 Add 18 to each side.

CPCTC

Answer: x = 25.5, y = 9

A. A

B. B

C. C

D. D

A. x = 4.5, y = 2.75

B. x = 2.75, y = 4.5

C. x = 1.8, y = 19

D. x = 4.5, y = 5.5

In the diagram, ΔFHJ ΔHFG. Find the values of x and y.

You will prove this!

Use the Third Angles Theorem

ARCHITECTURE A drawing of a tower’s roof is composed of congruent triangles all converging at a point at the top. If J K and mJ = 72, find mJIH.

GIVEN: ΔJIK ΔJIH

Use the Third Angles Theorem

Answer: mJIH = 36

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 85

B. 45

C. 47.5

D. 95

TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ΔKLM ΔNJL, KLM KML and mKML = 47.5, find mLNJ.

Prove That Two Triangles are Congruent

Write a two-column proof.

Prove: ΔLMN ΔPON

Prove That Two Triangles are Congruent

Proof:

Statements Reasons

Find the missing information in the following proof.

Prove: ΔQNP ΔOPN

Proof:ReasonsStatements

Q O, NPQ PNO1. 1. Given