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Understanding Isosceles and Equilateral Triangles: Concepts and Measures

This chapter delves into the properties of isosceles and equilateral triangles, focusing on congruent angles and segments. It explores how to identify unmarked congruent angles and segments using examples and the Triangle Sum Theorem. Readers will learn to find missing angle measures, apply the concepts through algebra, and understand key statements related to triangle congruence in various geometric contexts. Engaging exercises help reinforce understanding and application of these foundational principles in geometry.

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Understanding Isosceles and Equilateral Triangles: Concepts and Measures

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  1. Chapter 4.6 Isosceles and Equilateral Triangles

  2. Concept

  3. ___ BCA is opposite BA and A is opposite BC, so BCA  A. ___ Congruent Segments and Angles A. Name two unmarked congruent angles. Answer: BCAand A

  4. ___ BC is opposite D and BD is opposite BCD, so BC  BD. ___ ___ ___ ___ Answer: BC BD Congruent Segments and Angles B. Name two unmarked congruent segments.

  5. A. Which statement correctly names two congruent angles? A.PJM PMJ B.JMK JKM C.KJP JKP D.PML PLK

  6. A.JP PL B.PM PJ C.JK MK D.PM PK B. Which statement correctly names two congruent segments?

  7. Concept

  8. Find Missing Measures A. Find mR. Triangle Sum Theorem mQ = 60, mP = mR Simplify. Subtract 60 from each side. Answer:mR = 60 Divide each side by 2.

  9. Find Missing Measures B. Find PR. Answer:PR = 5 cm

  10. Example 2a A. Find mT. A. 30° B. 45° C. 60° D. 65°

  11. B. Find TS. A. 1.5 B. 3.5 C. 4 D. 7

  12. Find Missing Values ALGEBRA Find the value of each variable.

  13. Find the value of each variable. A.x = 20, y = 8 B.x = 20, y = 7 C.x = 30, y = 8 D.x = 30, y = 7

  14. Given:HEXAGO is a regular polygon. ΔONG is equilateral, N is the midpoint of GE, and EX || OG. Prove:ΔENX is equilateral. ___ Apply Triangle Congruence

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