Chapter 4.6. Isosceles and Equilateral Triangles Honors Geometry Chapter 4.6. Isosceles and Equilateral Triangles

Do Now Complete the following proof

Schedule Monday: Looking at Isosceles and Equilateral Triangles Tuesday: Finish looking at Isosceles and Equilateral Triangles/Quiz Review Wednesday: Quiz – types of triangles, angles in triangles, shape congruence, proving shape congruence and equilateral/isosceles triangles

Isosceles Triangles Legs: The two congruent sides Base: The third side of the triangle (opposite the vertex angle) Vertex Angle: The included angle between the legs. Base Angle: The two angles formed by the base and the congruent sides.

Example One: Legs? Base? Vertex Angle? Base Angles?

Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. ** NOTE: This is only for ISOSCELES TRIANGLES**

Let’s Prove it! Give: Triangle ABC; AC = BC Prove: <1 is congruent to <2

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

Example Two:

Example Three In the picture below, what segments are congruent?

You Try!

Example Four:

Example Five: Find the value of x and y

Example Six: Determine the missing angles and sides

You Try! Determine the missing angles/sides

Equilateral Triangle Theorems A triangle is equilateral if and only if it is equiangular

Equilateral Triangle Theorems Each angle of an equilateral triangle measures 60 degrees

Example Seven: Find

You Try! Find each measure

Example Eight:

Example Nine: An equiangular triangle has sides equal to 2x + 1, 8x – 5 and 5x – 2. What are the measures of the sides of the triangle?

Practice Problems Try some on your own/in table groups As always don’t hesitate to pull me aside to ask questions. OR ask your table mates– they are your greatest resource.

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