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# Holt McDougal Geometry 4-8 Isosceles and Equilateral Triangles Prove theorems about isosceles and...

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Holt McDougal Geometry 4-8 Isosceles and Equilateral Triangles Prove theorems about isosceles and equilateral triangles. Apply properties of isosceles and equilateral triangles. Objectives
Transcript
Slide 1Objectives
vertex angle
Isosceles and Equilateral Triangles
Recall that an isosceles triangle has at least two congruent sides. The congruent sides are called the legs. The vertex angle is the angle formed by the legs. The side opposite the vertex angle is called the base, and the base angles are the two angles that have the base as a side.
3 is the vertex angle.
1 and 2 are the base angles.
Holt McDougal Geometry
Isosceles and Equilateral Triangles
The Isosceles Triangle Theorem is sometimes stated as “Base angles of an isosceles triangle are congruent.”
Thus mF = 79°
Isosc. Thm.
Sum Thm.
x = 79
Holt McDougal Geometry
Thus mG = 22° + 44° = 66°.
mJ = mG
x = 22
Holt McDougal Geometry
Find mH.
Isosc. Thm.
Sum Thm.
x = 66
Thus mH = 66°
Find mN.
mP = mN
y = 8
Holt McDougal Geometry
Isosceles and Equilateral Triangles
The following corollary and its converse show the connection between equilateral triangles and equiangular triangles.
Holt McDougal Geometry
Find the value of x.
LKM is equilateral.
(2x + 32) = 60
2x = 28
Equilateral equiangular
Find the value of y.
NPO is equiangular.

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