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4.6 Isosceles Triangles

4.6 Isosceles Triangles. Objectives. Use properties of isosceles triangles Use properties of equilateral triangles. Properties of Isosceles Triangles. The  formed by the ≅ sides is called the vertex angle . The two ≅ sides are called legs . The third side is called the base .

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4.6 Isosceles Triangles

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  1. 4.6 Isosceles Triangles

  2. Objectives • Use properties of isosceles triangles • Use properties of equilateral triangles

  3. Properties of Isosceles Triangles • The  formed by the ≅ sides is called the vertex angle. • The two ≅ sides are called legs. The third side is called the base. • The two s formed by the base and the legs are called thebase angles. vertex leg leg base

  4. Isosceles Triangle Theorem • Theorem 4.9If two sides of a ∆ are ≅, then the s opposite those sides are ≅ (if AC ≅ AB, then B ≅ C). A B C

  5. The Converse of Isosceles Triangle Theorem • Theorem 4.10 If two s of a ∆ are ≅, then the sides opposite those s are ≅ (if B ≅ C, then AC ≅ AB).

  6. Name two congruent angles (not indicated). Example 2: Answer:

  7. Name two congruent segments (not indicated). By the converse of the Isosceles Triangle Theorem, the sides opposite congruent angles are congruent. So, Example 2: Answer:

  8. Your Turn: a. Name two congruent angles. Answer: b. Name two congruent segments. Answer:

  9. Properties of Equilateral ∆s • Corollary 4.3A ∆ is equilateral if it is equiangular. • Corollary 4.4Each  of an equilateral ∆measures 60°.

  10. EFG is equilateral, and bisects bisectsFindand Each angle of an equilateral triangle measures 60°. Since the angle was bisected, Example 3a:

  11. is an exterior angle of EGJ. Example 3a: Exterior Angle Theorem Substitution Add. Answer:

  12. EFG is equilateral, and bisects bisectsFind Example 3b: Linear pairs are supplementary. Substitution Subtract 75 from each side. Answer: 105

  13. ABC is an equilateral triangle. bisects Your Turn: a. Find x. Answer: 30 b. Answer: 90

  14. Assignment • Geometry: Pg. 219 #9 – 28, 36, 40 • Pre-AP Geometry: Pg. 219 #9 – 30, 35 – 37, & 40

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