ISOSCELE

S TRIA

NGLES

1Modified by Lisa Palen

PARTS OF AN ISOSCELES TRIANGLE

• An isosceles triangle is a triangle with at least two congruent sides.

• The congruent sides are called legs and the third side is called the base.

• The angles adjacent to the base are called base angles.

• The angle opposite the base is called the vertex angle.

1 and 2 are base angles.3 is the vertex angle.

and are legs. is the base.AC BCABAC BC 1 2

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ISOSCELES TRIANGLE THEOREMS

If two sides of a triangle are congruent, then the angles

opposite those sides are congruent.

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ISOSCELES TRIANGLE THEOREMS

If two angles of a triangle are congruent, then the sides

opposite those angles are congruent.

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EXAMPLE

x

50

Find the value of x.

By the Isosceles Triangle Theorem,the third angle must also be x.Therefore,x + x + 50 = 1802x + 50 = 1802x = 130x = 65

x

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MORE EXAMPLES

Find the value of x.

5050

x + 153x - 7

Since two angles are congruent, the sides opposite these angles must be congruent.

3x – 7 = x + 152x = 22x = 11

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EQUILATERAL AND EQUIANGULAR TRIANGLES

Corollary: If a triangle is equilateral, then …

it is equiangular.

.

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EQUILATERAL AND EQUIANGULAR TRIANGLES

Corollary: If a triangle is equiangular, then…

it is equilateral.

.

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WHAT IF ALL THE ANGLES IN A TRIANGLE ARE DIFFERENT?

Then the triangle is SCALENE because all of the sides are DIFFERENT too!

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