over lesson 11–1 a.a b.b c.c d.d 5-minute check 1 in the figure, a║b and t is a transversal. if...

Over Lesson 11–1

A. A

B. B

C. C

D. D

In the figure, a║b and t is a transversal. If m3 = 37°, find the measure of the other seven angles.

You have worked with triangles in the past (this year and previous years).

• Identify corresponding parts of congruent triangles.

• Identify congruent triangles.

• Congruent

• corresponding parts

Line segments that have the same length, or angles that have the same measure, or figures that have the same shape and size

Parts of congruent or similar figures that match

Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Name Corresponding Parts

Corresponding angles:D H, E G, F I

Answer: The congruence statement is ΔDEF ΔHGI.

Corresponding sides:DE HG, DF HI, EF GI

ΔDEF ?

A. Name the corresponding parts in the congruent triangles shown. Then complete the congruence statement ΔDEF Δ ? .

Name Corresponding Parts

Corresponding anglesS V, T W, U Z

B. If ΔSTU ΔVWZ, name the corresponding parts. Then complete the congruence statement ΔTSU Δ___?

Corresponding sidesST VW, TU WZ, US ZV

Answer: The congruence statement is ΔTSU ΔWVZ.

Use the order of the vertices in the congruence statement ΔSTU ΔVWZ to identify the corresponding parts.

A. A

B. B

C. C

D. D

A. B.

C. D.

A B C D

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A. Name the corresponding parts in the congruent triangles shown. Then complete the congruence statement ΔABC ____.?

A. A

B. B

C. C

D. D

A. ΔMON ΔEFG

B. ΔNMO ΔGEF

C. ΔONM ΔFEG

D. ΔNOM ΔFGE

B. If ΔMNO ΔEFG, what other congruence statement is true?

Find Missing Measures

F and C are corresponding angles, so they are congruent. Since mC = 50°, mF = 50°.

Answer: mF = 50°

A. CONSTRUCTION A brace is used to support a tabletop. In the figure, ΔABC ΔDEF. If mC = 50°, what is the measure of F?

Find Missing Measures

Answer: DF = 2 feet

B. CONSTRUCTION A brace is used to support a tabletop. In the figure, ΔABC ΔDEF. The length of AC is 2 feet. What is the length of DF?

AC and DF are corresponding sides, so they are congruent. Since AC = 2 feet, DF = 2 feet.

A. A

B. B

C. C

D. D

A. 44°

B. 46°

C. 90°

D. 136°

A. ART In the figure, ΔABC ΔDEF. What is the measure of B?

A. A

B. B

C. C

D. D

A. 158 in.

B. 68 in.

C. 44 in.

D. 22 in.

B. ART In the figure, ΔABC ΔDEF. What is the length of EF?

Identify Congruent Triangles

Determine whether the triangles shown are congruent. If so, name the corresponding parts and write a congruence statement.

The arcs indicate that M Q, N P, and O R.

The slash marks indicate that MN QP, NO PR, and MO QR.

Answer: Since all pairs of corresponding angles and sides are congruent, the two triangles are congruent. One congruence statement is ΔMNO ΔQPR.

A. A

B. B

C. C

D. D

A. yes; ΔABC ΔXYZ

B. yes; ΔABC ΔXZY

C. yes; ΔABC ΔZYX

D. No; the triangles are not congruent.

Determine whether the triangles shown are congruent. If so, write a congruence statement.