6-4: Isosceles Triangles

6-4: Isosceles Triangles NO NEED TO COPY Recall from 5-1 that an isosceles triangle has at least two congruent sides. There are two theorems dealing with isosceles triangles

6-4: Isosceles Triangles Theorem 6-2: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

6-4: Isosceles Triangles Theorem 6-3: The median from the vertex angle of an isosceles triangle IS ALSO the perpendicular bisector of the base AND IS ALSO the angle bisector of the vertex angle.

6-4: Isosceles Triangles Example Find the value of each variable in isosceles triangle DEF if EG is an angle bisector. Ignore the bisector for a second… This is an isosceles triangle Angles opposite equal sides are equal x = 49 Bring the bisector back in The angle bisector of an isosceles triangle is also the perpendicular bisector y = 90

6-4: Isosceles Triangles Your Turn Find the value of the variables in each triangle x = 65˚ y = 50˚ x = 90˚ y = 70˚

6-4: Isosceles Triangles Theorem 6-4: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

6-4: Isosceles Triangles Example In ABC, A  B and mA = 48. Find mC, AC, and BC. Finding mC A  B, so B also equals 48. 180˚ in a triangle. 48 + 48 + C = 180 96 + C = 180 C = 84

6-4: Isosceles Triangles Example In ABC, A  B and mA = 48. Find mC, AC, and BC. Finding AC & BC This is an isosceles triangle, so the two marked sides are equal. 4x = 6x – 5 -2x = -5 x = 5/2 (or 2.5) Plug back in to get AC/BC AC = 4(2.5) = 10 BC = 6(2.5) – 5 = 10

6-4: Isosceles Triangles Theorem 6-5: A triangle is only equilateral if it is equiangular

6-4: Isosceles Triangles Assignment Study Guide #6-4 and Practice Masters #6-4