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Isosceles and Equilateral Triangles

This section explores the properties of isosceles and equilateral triangles, focusing on important theorems such as the Isosceles Triangle Theorem and its converse. Through detailed examples, we learn how to determine angle measures and solve for unknown variables in various triangle configurations. Key exercises include finding the measures of angles in different scenarios involving isosceles triangles and applying theorems to solve geometric problems effectively.

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Isosceles and Equilateral Triangles

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  1. Isosceles and Equilateral Triangles Section 4.6 Objective: Use properties of isosceles triangles.

  2. Theorem 4.10Isosceles Triangle Theorem

  3. Theorem 4.11Converse of Isosceles Triangle Theorem

  4. Example 1

  5. Example 2 Find m <SRT

  6. Example 3 Find x and y.

  7. Example 4 Find x.

  8. Example 5 Find x and y.

  9. Example 6 • < Z • YZ

  10. Example 7 Find x and y.

  11. Example 8 In the figure AC BC and CD BD. • If m <ACB = 100, find the m <BDC. • If m <BAC = 30, find the m <BDC.

  12. Example 9 ΔKLN and ΔLMN are isosceles and m <JKN = 100. Find each measure. • m < LNM • m <M • m <LKN • m <J

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