1. Geometry 4.4 The Isosceles Triangle Theorems

2. Isosceles Triangle Vertex Angle Base Leg Base Angle

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 60 o 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. 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. 2. G F E D C B A A BCDE FG 3. Z Y XW V U T S S TU V WX Y Z

10. 3x xx 100 x x 50 70 x x 62 x x 3x x 100 70 x x x62 5. 6. 7. 8.9. 50

11. 1.2. vert3.4. StatementsReasons Given 2. Vert. angles congruent 3. Transitive 4. F E D 4 3 21 Given: Prove: Given: Prove:

12. 1. j2. 2. If lines, then corrs3.4.5.6. StatementsReasons j // k Given // implies corr. angles congruent Given 4. 5. 6. D E 4 3 21 C B A k j j // kGiven: Prove:

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 = ____. 12 3 4 5

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

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

17. A Few from the HW Together 13) Given: M is the midpoint of JK 1 = 2 Prove: JG = MK G J M K 1 2 77 ~ ~