Download IM2 Notes 6.5

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 twothirds of its 6 km base.
Lesson 1: Isosceles Triangles
Draw a line 3.5” long and another line 2” as
shown.
3.5” 2”
Lesson 1: Isosceles Triangles
Skipping down about 4 lines, draw a horizontal line about 4” long along a blue line.
3.5” 2”
Lesson 1: Isosceles Triangles
Construct Isosceles ∆ABC with base 3.5” and
side lengths 2” using a compass. Label the
side lengths.
A
3.5” 2”
3.5”
C
Lesson 1: Isosceles Triangles
Measure and label angles A and C. What do
you notice?
B
2”
A
3.5” 2”
2”
3.5”
C
Lesson 1: Isosceles Triangles
Isosceles ∆ Theorem: If 2 sides of a ∆ are ,
then the angles opposite the sides are .
B
2”
A
Example: If AB
3.5” 2”
2”
3.5”
BC, then / A
C
/ C.
Lesson 1: Isosceles Triangles
Converse Isosceles Triangle Theorem:
Example: if / A / C, then AB CB.
B
30°
A
30°
3.5”
C
Lesson 2: Congruent Segments and Angles
a. Name two unmarked congruent angles.
b. Name two unmarked congruent segments.
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”
Lesson 3: Equilateral Triangles
Example: If / A / B / C, then AB BC CA.
If AB BC CA, then m/ A = m/ B = m/ C = 60°.
B
2”
2”
A
2”
2”
C
Lesson 4: Finding Missing Measures
Find each measure.
a. m/ M
b. PN
Lesson 5: Find Missing Values
Find the value of each variable. Then find all
angle and length measures.
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°
Lesson 7: Finding Missing Values
Find the value of each variable. Then find the
measures of each angle and side length.
a. m/ BAC = m/ B = m/ BCA; AB = 2x + 11, BC =
6x – 9
b. AE = CE; m/ E = 100°, m/ EAC = 6y – 2, m/ ECA
= 4z + 20
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.
6.5: Do I Get It? Yes or No
1. Find each measure.
a. m/ Y
b. YZ
2. Find the value of each
variable.