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Geometry

Geometry. 4.4 The Isosceles Triangle Theorems. Isosceles Triangle. Vertex Angle. Leg. Leg. Base Angle. Base Angle. Base. The Isosceles Triangle Theorem. If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Iso. Thm. Corollary 1.

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Geometry

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  1. Geometry 4.4 The Isosceles Triangle Theorems

  2. Isosceles Triangle Vertex Angle Leg Leg Base Angle Base Angle Base

  3. The Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Iso. Thm.

  4. Corollary 1 An equilateral triangle is also equiangular. Why does this come from the Isosceles Triangle Theorem?

  5. Corollary 2 An equilateral triangle has three 60o angles.

  6. Corollary 3 The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. Proof Plan:

  7. Converse to Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Converse to Iso. Thm. 2 ways to remember which is which…

  8. Corollary An equiangular triangle is also equilateral.

  9. A C D B E F G S T U V Y W X Z Use the given information to name an isosceles triangle and its congruent base angles. 1. 2. Use the given information to name an isosceles triangle and its congruent legs.ZYXWVUTS 2. 3. A B C D E F G S 2. 3. T U V Y W X Z

  10. 70 x 62 50 x x x 100 3x x x 5. 6. x 3x x x 100 8. 9. 7. 70 50 62 x x x

  11. E F D 1 2 3 4 Given: Prove: 1. 2. vert 3. 4. Given: Prove:

  12. A 1 2 E D j 4 3 k C B Given: j // k Prove: 5. 4. 3. s , then corr 2. If lines 2. 6. 1. j

  13. HW P. 137-138 #1-10,13,14, 23-25, 27, 28

  14. A Few from the HW Together 23) a) If m<1 = 20, then m<3 = ____. m<4 = ____ and m<5 = ____. b) If m<1 = x, then m<3 = ____. m<4 = ____ and m<5 = ____. 4 3 5 2 1

  15. A Few From the HW 3) Find x. 74o 10 10 x 12

  16. A Few From the HW Together 5) Solve for x. 40o 40o 5x - 8 2x + 7

  17. A Few from the HW Together 13) Given: M is the midpoint of JK 1 = 2 Prove: JG = MK ~ 7 7 ~ J M 1 2 G K

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