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Notes 7-4 : Isosceles and Equilateral Triangles

On day 1, you learned that a triangle is isosceles if it has at least ______ _______________ __________. If it

has exactly two congruent sides, those sides are called the _________ of the triangle, and the third side

is called the ___________. The two angles adjacent to the base are the _________ _______________.

The third angle, or angle opposite the base is called the _____________ ______________.

Ex. 1 Name the vertex angle, base angles and the measures of both legs.

Vertex angle: __________

Base angles: _____________________

Measure of leg AB: ________________

Measure of leg BC:_________________

Partner Activity:

1. With a ruler construct an isosceles triangle below:

2. Measure the base angles, what do you notice about them?

3. With a protractor construct a triangle with two base angles that are congruent.

4. Measure the length of the sides, what do you notice about them?

5. What did you learn in this activity? What do you know about triangles with two congruent sides? What do you know about triangles with two congruent angles?

A C

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Isosceles Triangles:

1) If two sides of a triangle are congruent, then the base angles are congruent.

If AB≃AC , then ∠B≃∠C .

2) If two angles of a triangle are congruent, then the sides opposite them are congruent.

If ∠B≃∠C , then AB≃AC .

On day 1, you learned that an equilateral triangle has 3 _________________ sides.

We know an equilateral triangle has 3 congruent sides. What can you guess about a triangle that is equiangular?

Equilateral Triangles:

1) If a triangle is equilateral, then it is equiangular.

2) If a triangle is equiangular, then it is equilateral.

If equilateral triangles are equiangular, what is the measure of each angle in an equilateral triangle?

Ex. 2 Find the unknown measure(s). a. b.

Ex. 3 Solve for x and y. a. b. c.