The Isosceles Triangle Theorems

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Presentation transcript:

The Isosceles Triangle Theorems Base Angles and Opposite Sides Hypotenuse - Leg

Parts of an Isosceles Triangle

Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Given: Bisect angle A So by SAS So By C.P.C.T.

Corollary of Isosceles Triangle Theorem An equilateral triangle is also equiangular An equilateral triangle has three 60 degree angles. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.

Another Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent. What is this compared to the Isosceles Triangle Theorem? An equiangular triangle is also equilateral.

Solve for x and y

Solve for angles… 2,3,4 Given:

Hypotenuse – Leg (HL) In two right triangles if the hypotenuse and one leg are congruent, then the triangles are congruent. To use this you must show Right Triangles

Solve for v

Find the missing side