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Warm-Up 11/3/09 #7  Determine all ways to prove the triangles are congruent.


Warm Up 11/3/09 #7

A. Write the congruence statement. B. Name two pairs of corresponding angles. C. Name two pairs of corresponding sides. A

B

F

C

D E


ยง 4.4 The Isosceles Triangle Theorem (ITT) Objective: Find measures of isosceles triangles.


Recall: Isosceles Triangle    

Legs Base Base angles Vertex angle

B

A

C


ITT  Base angles of an isosceles triangle are congruent. B

 ALWAYS  ∠ A ≅ ∠C A

C


Converse of ITT (still called ITT)

 If two angles of a triangle are congruent, the sides opposite those angles are congruent. (AB = BC) B

A

C


Corollary’s  An equilateral triangle is also equiangular

 An equilateral triangle has three 60 º angles.


Another Corollary:  The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. B

 Angle B is bisected by segment BM  M is the midpoint of segment AC

C

A M


Proof!  Given: ∠1 ≅ ∠2  Prove: OK = OJ

1

J 3

O 4 K 2


Examples… Find the values of x for each… a)

30

x


X

B) ∠X ≅ ∠Y

2x - 4 Z 2x + 2 x+ 5 Y


Last one‌ C)

42

41

56

62 x


Homework  Page 137  1-8, 13, 14  ALL OR NOTHING!


Isosceles Triangles