Splash Screen. Lesson Menu Five-Minute Check (over Lesson 11–1) Then/Now New Vocabulary Key Concept: Corresponding Parts of Congruent Triangles Example.

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Presentation transcript:

Splash Screen

Lesson Menu Five-Minute Check (over Lesson 11–1) Then/Now New Vocabulary Key Concept: Corresponding Parts of Congruent Triangles Example 1: Name Corresponding Parts Example 2: Real-World Example: Find Missing Measures Example 3: Identify Congruent Triangles

Over Lesson 11–1 5-Minute Check 1 A.37° B.43° C.137° D.143° In the figure, a║b and t is a transversal. If m  3 = 37°, find m  8.

Over Lesson 11–1 5-Minute Check 2 A.37° B.43° C.137° D.143° In the figure, a║b and t is a transversal. If m  3 = 37°, find m  7.

Over Lesson 11–1 5-Minute Check 3 A.m  A = 156°, m  B = 24° B.m  A = 107°, m  B = 73° C.m  A = 73°, m  B = 107° D.m  A = 34°, m  B = 146° If  A and  B are supplementary, m  A = 3x – 7, and m  B = 2x – 3, what is the measure of each angle?

Over Lesson 11–1 5-Minute Check 4 A.52.7 B.47.3 C.42.7 D.37.3 What is the value of x?

Over Lesson 11–1 5-Minute Check 5 A.  3 and  6 B.  3 and  2 C.  3 and  5 D.  3 and  4 Which angles are alternate interior angles?

Then/Now You identified triangles with congruent sides. (Lesson 9–3) Identify corresponding parts of congruent triangles. Identify congruent triangles.

Vocabulary congruent corresponding parts

Concept

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.

Example 1 CYP A A.B. C.D. A. Name the corresponding parts in the congruent triangles shown. Then complete the congruence statement ΔABC  ____. ?

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.

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?

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.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