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

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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.”

Reading Math

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.

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.”

Reading Math

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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