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A B C D. In the figure, a ║ b and t is a transversal. If m 3 = 37°, find the measure of the other seven angles. 5-Minute Check 1. Splash Screen. You have worked with triangles in the past (this year and previous years). Identify corresponding parts of congruent triangles.
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A B C D In the figure, a║band t is a transversal. If m3 = 37°, find the measure of the other seven angles. 5-Minute Check 1
You have worked with triangles in the past (this year and previous years). • Identify corresponding parts of congruent triangles. • Identify congruent triangles. Then/Now
Congruent Line segments that have the same length, or angles that have the same measure, or figures that have the same shape and size • corresponding parts Parts of congruent or similar figures that match Vocabulary
Congruent Parts of Congruent Triangles are Congruent (CPCTC) Concept
ΔDEF ? Corresponding sides:DE HG, DF HI, EF GI Name Corresponding Parts A.Name the corresponding parts in the congruent triangles shown. Then complete the congruence statement ΔDEF Δ ? . Corresponding angles:D H, E G, F I Answer: The congruence statement is ΔDEF ΔHGI. Example 1 A
B.If ΔSTU ΔVWZ, name the corresponding parts. Then complete the congruence statement ΔTSUΔ___ ? Corresponding sidesST VW, TU WZ, US ZV Name Corresponding Parts Use the order of the vertices in the congruence statement ΔSTU ΔVWZ to identify the corresponding parts. Corresponding anglesS V, T W, U Z Answer: The congruence statement is ΔTSU ΔWVZ. Example 1 B
A B C D A. Name the corresponding parts in the congruent triangles shown. Then complete the congruence statement ΔABC ____. ? A. B. C.D. Example 1 CYP A
A B C D B. If ΔMNO ΔEFG, what other congruence statement is true? A.ΔMON ΔEFG B.ΔNMO ΔGEF C.ΔONM ΔFEG D.ΔNOM ΔFGE Example 1 CYP B
Find Missing Measures A. CONSTRUCTION A brace is used to support a tabletop. In the figure, ΔABC ΔDEF. If mC = 50°, what is the measure of F? F and C are corresponding angles, so they are congruent. Since mC = 50°, mF = 50°. Answer:mF = 50° Example 2 A
B. CONSTRUCTIONA 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. Answer:DF = 2 feet Find Missing Measures Example 2 B
A B C D A. ART In the figure, ΔABC ΔDEF. What is the measure of B? A. 44° B. 46° C. 90° D. 136° Example 2 CYP A
A B C D B. ART In the figure, ΔABC ΔDEF. What is the length of EF? A. 158 in. B. 68 in. C. 44 in. D. 22 in. Example 2 CYP B
The slash marks indicate that MN QP, NO PR, and MO QR. 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. Answer: Since all pairs of corresponding angles and sides are congruent, the two triangles are congruent. One congruence statement is ΔMNO ΔQPR. Example 3
A B C D Determine whether the triangles shown are congruent. If so, write a congruence statement. A. yes; ΔABC ΔXYZ B.yes;ΔABC ΔXZY C. yes; ΔABC ΔZYX D.No; the triangles are not congruent. Example 3 CYP