Geometry 4 4 The Isosceles Triangle Theorems Isosceles

Geometry 4. 4 The Isosceles Triangle Theorems

Isosceles Triangle Vertex Angle Leg Base Angle

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

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

Corollary 2 An equilateral triangle has three 60 o angles.

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

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…

Corollary An equiangular triangle is also equilateral.

Use the given information to name an isosceles triangle and its congruent base angles. 1. A A 2. C C BB D D FF EE GG Use the given information to name an isosceles triangle and its congruent legs. ZYXWVUTS 3. 2. S S 2. T T 3. VV U U W W XX Z Z YY

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

E Given: Prove: D 4 2. vert 1. 4. 3. Statements Reasons Given 2. Given: Vert. angles congruent Prove: 3. Transitive 4. 1 2 F 3

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

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

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

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

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

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