Download Geometry Pg. 181-184 Assignment #16 Isosceles and Equilateral

Pg. 181-184
Geometry
Assignment #16
Isosceles and Equilateral
Triangles
1.
Given isosceles Δ XYZ where XY = YZ. If XY = 3m – 7 and XZ = 2m + 1, find the
perimeter of the triangle in terms of m.
2.
Given isosceles Δ ABC where the vertex angle A = 70º. Find m∠B.
3.
Given isosceles Δ MNP where MN = NP. If m∠N = 40° , find m∠P.
4.
Given isosceles Δ EMP. If EM = EP, name the base angles.
5.
Given isosceles Δ MOB. If MO = OB, name the vertex angle.
6.
In Δ ABC, if AB = AC, m∠B = 3x + 15 , and m∠C = 7x − 5 , find m∠B and m∠C.
7.
In equilateral Δ DEF, m∠D = 3x + y , m∠E = 2x + 40 , and m∠F = 2y . Find x, y, m∠D ,
m∠E , and m∠F.
8.
The degree measure of a base angle of an isosceles triangle exceeds twice the degree
measure of the vertex angle by 15. Find the degree measure of the vertex angle.
9.
True or False: Every equilateral triangle is equiangular.
10. What does the Isosceles Triangle Theorem state? Is the converse also true?
11. The perimeter of an isosceles triangle is 71 centimeters. The measure of one of the sides is
22 centimeters. What are all the possible measures of the other two sides?
12. Tina wants to sew a piece of fabric into a scarf in the shape of an
isosceles triangle, as shown in the accompanying diagram. Find the
values of x and y.
12
13. In ∆ABC, ∠A ≅ ∠B , m∠A = 48, AC = 4x and BC = 6x − 5 . Find m∠C ,
and the lengths of AC and BC .
14. An equilateral triangle has a perimeter of 78. Find the value of each side of the triangle.
15. An isosceles triangle has a perimeter of 22 inches. The two equal sides are each 2 inches
longer than the third side. How long is the third side?
Island Trees Math Department
A
C
16. True or False: ΔABC is isosceles
22°
16
78°
17. Solve for x: x 2 + ( x − 1) = ( x + 1)
2
2
B
18
B
18. AB ⊥ BC , m∠A = 44° , m∠E = 21° .
Find m∠EDC.
D
C
A
E
1.
2.
3.
4.
5.
6.
7.
8.
9.
8m – 13
55
70
∠M ≅ ∠P
vertex = ∠O
30, 30
x = 10, y = 30, angles = 60
30
True
10.
11.
12.
13.
14.
15.
16.
17.
18.
Explain
22, 22, 27 or 22, 24.5, 24.5
x = 96, y = 42
∠C = 84 , AC = 10 , BC = 10
26
6
No
x = {0, 4}
113
Island Trees Math Department