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.

Exit Ticket