Notes 4-9: Isosceles and Equilateral Triangles

Name _____________________ Date _______________ Period __________

What is an isosceles triangle? ________________________________________________

 The congruent sides are called the legs.

 The third side is called the base.

 The angle opposite the base is called the vertex angle.

 The angles opposite the congruent sides are called the base angles.

(These are the angles that are adjacent to the base.)

If a triangle has two congruent sides, does the triangle also have two congruent angles?

Isosceles Triangle Theorem

If ________sides of a triangle are congruent, then the ______________the sides are congruent.

,RT RS

then T  S.

Converse of Isosceles Triangle Theorem

If __________________of a triangle are congruent, then the ________________those angles are

congruent.

If N  M, then

.LN LM

You can use these theorems to find angle measures in isosceles triangles.

Example

Find m∠E in DEF.

m∠D  m∠E Isosceles  Thm.

5x  3x + 14 Substitute the given values.

Solve for x.

Find m∠E

Find each angle measure.

1. m∠C  _____________________ 2. m∠Q  _____________________

3. m∠H  _____________________ 4. m∠M  _____________________

You can use these theorems to find values in equilateral triangles.

Example

Find x in STV.

STV is equiangular. Equilateral  → equiangular 

7x + 4  60 The measure of each ∠ of an

equiangular  is 60.

Solve for x.

Find each value.

5. n  _____________________ 6. x  _____________________

7. VT  _____________________ 8. MN  __________________

Equilateral Triangle Corollary

If a triangle is equilateral, then it is equiangular.

(equilateral   equiangular )

Equiangular Triangle Corollary

If a triangle is equiangular, then it is equilateral.

(equiangular   equilateral )

If A   B  C, then

AB BC CA