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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