Download Notes: Isosceles Triangles

Modified by Lisa Palen
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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.
AC and BC are legs.
AB is the base.
AC  BC
1 and 2 are base angles.
3 is the vertex angle.
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1  2
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
Find the value of x.
By the Isosceles Triangle Theorem,
the third angle must also be x.
Therefore,
x + x + 50 = 180
2x + 50 = 180
2x = 130
x = 65
50
x
x
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MORE EXAMPLES
Find the value of x.
3x - 7
50
x + 15
50
Since two angles are congruent, the
sides opposite these angles must be
congruent.
3x – 7 = x + 15
2x = 22
x = 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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