Isosceles and Equilateral Triangles

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Presentation transcript:

Isosceles and Equilateral Triangles Lesson 4-5

Isosceles Triangles Legs – the congruent sides of an isosceles triangle Base – the third side of an isosceles triangle Vertex angle – formed by the congruent sides Base angles – the angles adjacent to the base Vertex angle legs base base angles

Thm 4-3 Isosceles Triangle Thm. Q U E Two sides of a triangle are congruent if and only if angles opposite those sides are congruent. Then ÐQ @ ÐE

Thm 4-5 U Q E M QE ^ UM UM bisects QE The bisector of the vertex angle of an isosceles triangles is the perpendicular bisector of the base. M QE ^ UM UM bisects QE

Using the Isosceles Triangle Thm. Explain why DABC is isosceles.

Using Algebra with the Isosceles Triangle Thm Suppose that mL = y. Find the values of x and y. x = 90 and y = 45.

An angle exterior to the vertex of an isosceles triangle measures 80 An angle exterior to the vertex of an isosceles triangle measures 80. Find the angle measures of the triangle. 80° 1 3 2

Equilateral Triangles If you have an Equilateral Triangle, then all the angles are congruent. If you have an Equiangular Triangle, then all the sides are congruent.