Transcript Isosceles and Equilateral Triangles LESSON 4-5 Additional Examples Explain why ABC is isosceles. ABC and XAB are alternate interior angles formed by XA, BC, and the.

Isosceles and Equilateral Triangles
LESSON 4-5
Additional Examples
Explain why
ABC is isosceles.
ABC and XAB are alternate interior angles
formed by XA, BC, and the transversal AB. Because
XA || BC, ABC XAB.
The diagram shows that XAB ACB. By the
Transitive Property of Congruence, ABC ACB.
You can use the Converse of the Isosceles Triangle
Theorem to conclude that AB AC.
By the definition of an isosceles triangle,
isosceles.
ABC is
Quick Check
HELP
GEOMETRY
Isosceles and Equilateral Triangles
LESSON 4-5
Additional Examples
Suppose that mL = y. Find the values of x and y.
MO
The bisector of the vertex angle of an
isosceles triangle is the perpendicular
bisector of the base.
x = 90
Definition of perpendicular
mN = mL Isosceles Triangle Theorem
mL = y
Given
mN = y
Transitive Property of Equality
mN + mNMO + mMON = 180 Triangle Angle-Sum Theorem
y + y + 90 = 180 Substitute.
2y + 90 = 180 Simplify.
2y = 90
Subtract 90 from each side.
y = 45
Divide each side by 2.
Quick Check
Therefore, x = 90 and y = 45.
HELP
LN
GEOMETRY
Isosceles and Equilateral Triangles
LESSON 4-5
Additional Examples
Suppose the raised garden bed is a regular hexagon.
Suppose that a segment is drawn between the endpoints of the angle
marked x. Find the angle measures of the triangle that is formed.
Because the garden is a regular hexagon, the sides
have equal length, so the triangle is isosceles.
By the Isosceles Triangle Theorem, the unknown
angles are congruent.
Example 4 found that the measure of the angle
marked x is 120°. The sum of the angle measures of
a triangle is 180°.
If you label each unknown angle y, 120 + y + y = 180.
120 + 2y = 180
2y = 60
y = 30
So the angle measures in the triangle are 120°, 30° and 30°.
HELP
Quick Check
GEOMETRY