Download 4-5:Isosceles and Equilateral Triangles

4-5:Isosceles and
Equilateral Triangles
Properties of Isosceles Triangles
Vertex
Leg
Vertex:
the meeting of the two equal legs
Leg
Base:
opposite vertex angle
Base
Angle
Base
Base
Angle
Base Angles:
opposite the equal legs
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Theorem 4‐3: Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Theorem 4‐4: Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Complete Got It? #1 p. 251
Theorem 4‐5:
If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base.
Complete Got It? #2 p. 252
x  63
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Corollary to Theorem 4‐3:
A
If a triangle is equilateral, then the triangle is equiangular.
C
B
Corollary to Theorem 4‐4:
A
If a triangle is equiangular, then the triangle is equilateral.
C
B
Ex. 1:
B
Given: AB  BC
Prove: BAC  ECD
A
Statement
Justification
C
D
E
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Ex. 2
In circle P below, mP  37. What is mPAB ?
180  37  143  71.5
2
37°
P
B
A
Ex. 3
In isosceles triangle ABC below, mB  118 and the bisectors of angles A and C intersect at point E. Find mAEC.
180  118 62

 31
2
2
31
 15.5
2
180  15.5  2   180  31
 149
A
C
15.5
15.5
149
E
118
B
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Homework: p. 254 #6‐12 even, 22, 23, 25, 27, 28, 30‐
32, 37‐40.
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