ISOSCELES TRIANGLES 1 Modified 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. 2

ISOSCELES TRIANGLE THEOREMS If two sides of a triangle are congruent, then the angles opposite those sides are congruent. 3

ISOSCELES TRIANGLE THEOREMS If two angles of a triangle are congruent, then the sides opposite those angles are congruent. 4

EXAMPLE By the Isosceles Triangle Theorem, the third angle must also be x. Therefore, x + x + 50 = 180 2x + 50 = 180 2x = 130 x = 65 xx 5

MORE EXAMPLES Since two angles are congruent, the sides opposite these angles must be congruent. 3x – 7 = x x = 22 x = 11 6

EQUILATERAL AND EQUIANGULAR TRIANGLES Corollary: If a triangle is equilateral, then … it is equiangular.. 7

EQUILATERAL AND EQUIANGULAR TRIANGLES Corollary: If a triangle is equiangular, then… it is equilateral.. 8

WHAT IF ALL THE ANGLES IN A TRIANGLE ARE DIFFERENT? Then the triangle is SCALENE because all of the sides are DIFFERENT too! 9