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Transcript 
Unit 4: Triangle Congruence
4.8 Isosceles and Equilateral
Triangles (Part 1)
Warm Up 11/22 (HW #21 [4.8] Page 277 #s 13 – 20)
1. Find each angle measure.
A
60°; 60°; 60°
2. Solve x2 + 5x + 6 = 0 for x.
x = – 3 and x = – 2
B
C
Objectives
Prove theorems about isosceles triangles.
Apply properties of isosceles triangles.
*Standard 12.0 Students find and use measures of sides
and of interior and exterior angles of triangles and
polygons to classify figures and solve problems.
(see page 273)
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.
(see page 273)
Example 2A: Finding the Measure of an Angle (see page 274)
Find mF.
mF = mD = x°
mF + mD + mA = 180
x + x + 22 = 180
2x = 158
x = 79
Isosc. ∆ Thm.
∆ Sum Thm.
Substitute the given values.
Simplify and subtract 22 from
both sides.
Divide both sides by 2.
Thus mF = 79°
Check It Out! Example 2A (see page 274)
Find mH.
mH = mG = x°
mH + mG + mF = 180
x + x + 48 = 180
2x = 132
x = 66
Thus mH = 66°
Isosc. ∆ Thm.
∆ Sum Thm.
Substitute the given values.
Simplify and subtract 48
from both sides.
Divide both sides by 2.
1. Find x.
A
B
C
D
Example 2B: Finding the Measure of an Angle (see page 274)
Find mG.
mJ = mG
(x + 44) = 3x
44 = 2x
x = 22
Isosc. ∆ Thm.
Substitute the given values.
Simplify x from both sides.
Divide both sides by 2.
Thus mG = 22° + 44° = 66°
mG = 66°
Check It Out! Example 2B (see page 274)
Find mN.
mP = mN
Isosc. ∆ Thm.
(8y – 16) = 6y
Substitute the
given values.
2y = 16
Subtract 6y and
add 16 to both
sides.
y = 8
Divide both sides
by 2.
Thus mN = 6(8) = 48°.
mN = 48°
2. Find mR and mP.
3. The vertex angle of an isosceles triangle measures
(a + 15)°, and one of the base angles measures 7a°.
Find a and each angle measure.
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