1. 6.5 Notes: Isosceles and Equilateral Triangles
Lesson Objective: Use properties of isosceles and equilateral triangles.
CCSS: G.CO.10, 12
You will need: compass, ruler, colored pens
Real-World App: What are the angles of the gable of a house?
This is Jeopardy!!!:  This is the perimeter of an Isosceles triangular park if its legs are two- thirds of its 6 km base.

2. Lesson 1: Isosceles Triangles
Draw a line 3.5” long and another line 2” as shown.
3.5” 2”

3. Lesson 1: Isosceles Triangles
Skipping down about 4 lines, draw a horizon-tal line about 4” long along a blue line.
3.5” 2”

4. Lesson 1: Isosceles Triangles
Construct Isosceles ∆ABC with base 3.5” and side lengths 2” using a compass. Label the side lengths.
A ” C
3.5” 2”

5. Lesson 1: Isosceles Triangles
Measure and label angles A and C. What do you notice? B
2” ”
A ” C
3.5” 2”

6. Lesson 1: Isosceles TrianglesB
2” ”
A ” C
Example: If AB BC, then / A / C.
3.5” 2”
Isosceles ∆ Theorem: If 2 sides of a ∆ are , then the angles opposite the sides are .

7. Lesson 1: Isosceles TrianglesB
30° °
A ” C
Converse Isosceles Triangle Theorem:
Example: if / A / C, then AB CB.

8. Lesson 2: Congruent Segments and Angles
Name two unmarked congruent angles.
Name two unmarked congruent segments.

9. Lesson 3: Equilateral Triangles
With only a compass and ruler, construct a 2” equilateral triangle. Start about 6-7 lines down. Work with your partner if you don’t know how to do this. 2”

10. Lesson 3: Equilateral TrianglesB
2” ”
2” A ” C
Example: If / A / B / C, then AB BC CA.
If AB BC CA, then m/ A = m/ B = m/ C = 60°.

11. Lesson 4: Finding Missing Measures
Find each measure.
m/ M PN

12. Lesson 5: Find Missing Values
Find the value of each variable. Then find all angle and length measures.

13. Lesson 6: Real-World App
The exterior angle of an Isosceles gable of a house is shown. What are the measures the interior angles of the gable?
145°

14. Lesson 7: Finding Missing Values
Find the value of each variable. Then find the measures of each angle and side length.
m/ BAC = m/ B = m/ BCA; AB = 2x + 11, BC = 6x – 9
AE = CE; m/ E = 100°, m/ EAC = 6y – 2, m/ ECA = 4z + 20

15. 6.1(b): Do I Get It? Yes or No
1. Find m/ 1 on the truck below.
2. Find the value of x in the figure above right. Then find the measure of each angle.

16. 6.5: Do I Get It? Yes or No
1. Find each measure.
m/ Y YZ
Find the value of each
variable.