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 m  3 = 37°, find the measure of the other seven angles.

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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 m  3 = 37°, find the measure of the other seven angles.

Splash Screen

Then/Now You have worked with triangles in the past (this year and previous years). Identify corresponding parts of congruent triangles. Identify congruent triangles.

Vocabulary 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

Concept Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Example 1 A 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 ?.

Example 1 B Name Corresponding Parts Corresponding angles  S   V,  T   W,  U   Z B. If ΔSTU  ΔVWZ, name the corresponding parts. Then complete the congruence statement ΔTSU  Δ___ ? Corresponding sides ST  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 Example 1 CYP A A.B. C.D. A. Name the corresponding parts in the congruent triangles shown. Then complete the congruence statement ΔABC  ____. ?

A.A B.B C.C D.D Example 1 CYP B A.ΔMON  ΔEFG B.ΔNMO  ΔGEF C.ΔONM  ΔFEG D.ΔNOM  ΔFGE B. If ΔMNO  ΔEFG, what other congruence statement is true?

Example 2 A Find Missing Measures  F and  C are corresponding angles, so they are congruent. Since m  C = 50°, m  F = 50°. Answer: m  F = 50° A. CONSTRUCTION A brace is used to support a tabletop. In the figure, ΔABC  ΔDEF. If m  C = 50°, what is the measure of  F?

Example 2 B 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 Example 2 CYP A 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 Example 2 CYP B 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?

Example 3 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. Example 3 CYP Determine whether the triangles shown are congruent. If so, write a congruence statement.

End of the Lesson