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

2. Do Now
Complete the following proof

3. 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

4. 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.

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

6. 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**

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

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

9. Example Two:

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

11. You Try!

12. Example Four:

13. Example Five:
Find the value of x and y

14. Example Six:
Determine the missing angles and sides

15. You Try!
Determine the missing angles/sides

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

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

18. Example Seven:
Find

19. You Try!
Find each measure

20. Example Eight:

21. 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?

22. 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.

24. Exit Ticket