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Understanding Congruent Triangles: Finding Missing Angles and Parts

This lesson explores the concept of congruent triangles, focusing on identifying corresponding parts and measuring missing angles. Given a transversal and angle measures, students will learn to find all angles in congruent triangles. The lesson reinforces vocabulary like congruent and corresponding parts, while also presenting practical examples of determining congruence statements. Through engaging exercises, learners will solidify their understanding of triangle properties, enabling them to recognize congruence visually and numerically in various geometric scenarios.

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Understanding Congruent Triangles: Finding Missing Angles and Parts

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  1. A B C D In the figure, a║band t is a transversal. If m3 = 37°, find the measure of the other seven angles. 5-Minute Check 1

  2. Splash Screen

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

  4. 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

  5. Congruent Parts of Congruent Triangles are Congruent (CPCTC) Concept

  6. 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

  7. B.If ΔSTU ΔVWZ, name the corresponding parts. Then complete the congruence statement ΔTSUΔ___ ? 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 anglesS V, T  W, U  Z Answer: The congruence statement is ΔTSU  ΔWVZ. Example 1 B

  8. 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

  9. 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

  10. Find Missing Measures 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? F and C are corresponding angles, so they are congruent. Since mC = 50°, mF = 50°. Answer:mF = 50° Example 2 A

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. End of the Lesson

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