Download 4.9 Isosceles and Equilaterl Triangles

4-9 Isosceles and Equilateral Triangles
Objectives: G.CO.10: Prove theorems about triangles
For the Board: You will be able to prove and apply the properties of isosceles and equilateral triangles.
Bell Work 4.9:
1. Find each angle measure.
True or false. If false explain.
2. Every equilateral triangle is isosceles.
3. Every isosceles triangle is equilateral.
A
Anticipatory set:
When an isosceles triangle has only two congruent sides, these sides are called legs.
The third side is the base of the isosceles triangle.
The two angles adjacent to the base and opposite the legs are the base angles.
The angle opposite the base is the vertex angle.
C
B
Base Angles Theorem
If two sides of a triangle are congruent then the angles opposite them are congruent.
Given: AB  AC
Prove: <B  <C.
Base Angles Converse Theorem
If two angles of a triangle are congruent then the sides opposite them are congruent.
Given: <B  <C
Prove: AB  AC.
Open the book to page 286 and read example 2.
Example: Find each angle or side measure.
G
E
a. m<F
b. m<G
22°
H
D
3x°
J
F
180 – 22 = 158/2 = 79°
A
c. AB
(x + 44)°
x + 44 = 3x
x = 22
d. LM
44 = 2x
m<G = 22 + 44 = 66°
L
(2x + 9)°
M
15
5x°
B
AB = 15
C
N
2x + 9 = 5x
x=3
3x = 9
LM = 2(3) + 9 = 15°
White Board Activity:
Practice: Find each angle or side measure.
a. m<H 48° F
G
H
m<H = (180 – 48)/2 = 64°
F
c. FG
b. m<N
M 6y°
(8y – 16)°
P
6y = 8y – 16
y=8
M
d. PN
2y = 16
m<N = 8(8) – 16 = 48°
N
7x
41
G
N
9x - 24
P
H
FG = 41
7x = 9x – 24
X=6
2x = 12
PN = 9(6) – 24 = 30
Corollary to the Base Angles Theorem
A triangle is equilateral if and only if it is equiangular.
Recall: Each angle of an equilateral triangle is 60°.
Open the book to page 287 and read example 3.
Example: Find each value.
L
a. x
(2x + 32)°
O
b. y
4y + 12
5y - 6
M
K
White Board Activity:
Practice: Find each value.
L
a.
(3x + 24)°
5y – 6 = 4y + 12
K
M
Assessment:
Question Student Pairs.
y = 18
O
b.
6y - 5
3x + 24 = 60
3x = 36
x = 12
P
N
2x + 32 = 60
2x = 28
x = 14
3y + 21
N
6y – 5 = 3y + 22
y=9
P
3y = 27
Independent Practice:
Text: pgs. 288 – 290 prob. 3 – 10 , 13 – 20, 27 – 29.
Explorations: pg. 183 prob. 3–10.
For a Grade:
Text: pgs. 288 – 290 prob. 8, 14, 18, 28.