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
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 Three• In the picture below, what segments are congruent?
Example Five: • Find the value of x and y
Example Six: • Determine the missing angles and sides
You Try! • Determine the missing
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
Example Seven: • Find
You Try! • Find each measure
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.