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4-8 Isosceles and Equilateral Triangles
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Pg. 277(13-14; 16-25; 43 why4; 51-53)
Holt McDougal Geometry
4-8 Isosceles and Equilateral Triangles
Essential Questions
1) How do you apply properties of
isosceles and equilateral triangles?
Holt McDougal Geometry
4-8 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
4-8 Isosceles and Equilateral Triangles
Holt McDougal Geometry
4-8 Isosceles and Equilateral Triangles
Example 1A: Finding the Measure of an Angle
Find mF.
mF = mD = x°
Isosc. ∆ Thm.
mF + mD + mE = 180 ∆ Sum Thm.
Substitute the
x + x + 22 = 180 given values.
Simplify and subtract
2x = 158 22 from both sides.
x = 79 Divide both
sides by 2.
Thus mF = 79°
Holt McDougal Geometry
4-8 Isosceles and Equilateral Triangles
Example 1B: Finding the Measure of an Angle
Find mG.
mJ = mG Isosc. ∆ Thm.
(x + 44) = 3x
44 = 2x
Substitute the
given values.
Simplify x from
both sides.
Divide both
sides by 2.
Thus mG = 22° + 44° = 66°.
x = 22
Holt McDougal Geometry
4-8 Isosceles and Equilateral Triangles
The following corollary and its converse show the
connection between equilateral triangles and
equiangular triangles.
Holt McDougal Geometry
4-8 Isosceles and Equilateral Triangles
Holt McDougal Geometry
4-8 Isosceles and Equilateral Triangles
Example 2A: Using Properties of Equilateral
Triangles
Find the value of x.
∆LKM is equilateral.
Equilateral ∆  equiangular ∆
(2x + 32) = 60
2x = 28
x = 14
Holt McDougal Geometry
The measure of each  of an
equiangular ∆ is 60°.
Subtract 32 both sides.
Divide both sides by 2.
4-8 Isosceles and Equilateral Triangles
Example 2B: Using Properties of Equilateral
Triangles
Find the value of y.
∆NPO is equiangular.
Equiangular ∆  equilateral ∆
Definition of
5y – 6 = 4y + 12
equilateral ∆.
y = 18
Holt McDougal Geometry
Subtract 4y and add 6 to
both sides.
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