Name _____________________________________________________
Period ______
3.6 Isosceles and Equilateral Triangles
Solve for any variables given the type of triangle. Show all algebraic work.
1. Equilateral Triangle
2. Equilateral Triangle
3. Equilateral Triangle
H
B
M
2y+6
3 in
(2x)°
2y+2
4y-2
A
60°
L
4
(4y-5) in
(6x+8)°
G
5x-3
I
P
C
̅̅̅̅ ≅ 𝐴𝐷
̅̅̅̅
4. Isosceles Triangle with 𝐴𝐵
̅̅̅̅ ≅ 𝑋𝑌
̅̅̅̅
5. Isosceles Triangle with 𝑋𝑍
̅̅̅̅̅
̅̅̅̅̅ ≅ 𝑀𝑂
6. Isosceles Triangle with 𝑀𝑁
M
Z
A
3x+5
5y-6
W
D
5x-11
C
B
Y
18+2y
8x+24
2x-18
N
O
X
(3y+30)°
Given the information, find the following. Show all algebraic work.
̅̅̅̅ is a median of equilateral ∆𝐴𝐵𝐶.
7. 𝐴𝐷
̅̅̅̅ ≅ 𝐸𝐹
̅̅̅̅ is an angle bisector of isosceles ∆𝐸𝐹𝐺 with 𝐸𝐺
̅̅̅̅ .
8. 𝐸𝐻
A
F
(7x-23)°
2x + 25
3x – 10
E
E
-12y+13
(8x+10)°
H
(2y + 50)°
B
D
-7y-27
C
(5y – 17)°
x=
x=
y=
y=
AB =
GF =
𝑚∠BDE =
𝑚∠EFH =
𝑚∠EDA =
𝑚∠HEF =
9. In what type of triangle are the medians, altitudes,
angle bisectors, and perpendicular bisectors from
any vertex the same line?
a) Scalene Triangle
b) Isosceles Triangle
c) Equilateral Triangle
d) All of the Above
e) None of the Above
G
10. ̅̅̅̅
𝐴𝐷 is a median of ∆𝐴𝐵𝐶. Find x and ̅̅̅̅
𝐵𝐷 .
A
B
C
𝑥 2 + 4𝑥 D 3𝑥 + 30