1. Practice Quiz
Triangles

2. 1
If PRQ is an isosceles triangle with PQ = PR, find the measure of QPX.
∆PRQ: Isosceles Triangle
The base angles are equal.
QPX: Exterior Angle
60 ?

3. ? In the figure, if ABC is the same size and shape as ABD,2
In the figure, if ABC is the same size and shape as ABD,
then the degree measure of BAD =
75 ?

4. A B In the figure, if side RS = ST and x = 115°,3
In the figure, if side RS = ST and x = 115°,
what is the measure of angle w?
Base
Angles
A = B
Isosceles
Triangle A B

5. Supplementary Angles of base angles are equal.3
In the figure, if side RS = ST and x = 115°,
what is the measure of angle w?
T = 115
Supplementary Angles of base angles are equal.
Base
Angles
A = B A B
w and T are
Vertical Angles
115

6. 2z = 70 + z – z – z z = 70 70 2z In the figure, if x = 2z and y = 70,
what is the value of z? 4 70 2z
2z = 70 + z
Exterior Angles
Rule
– z
– z
z = 70

7. ? = 180° – 145° ? = 35° ? In the figure, if side AB = AC and
w = 145°, what is the measure of x? ?
145°
? = 180° – 145°
? = 35°

8. x = 35° + 35° x = 70° 35° 35° In the figure, if side AB = AC and
w = 145°, what is the measure of x?
Isosceles
Triangle
35°
35°
145°
Exterior Angles
Rule
x = 35° + 35°
x = 70°

9. 6
If the ratio of the angles of a triangle is 2:3:4, what is the degree measure of the largest angle?
Largest Angle 4x
4(20)
= 80

10. B Ratio Vertex : Base : Base 1 : 4 : 4 A C
In an isosceles triangle, if the ratio of the vertex angle to the base angle is 1:4, what is the degree measure of the base angle? 7 B
Vertex Angle: B
Base Angle: A
Base Angle: C
Ratio
Vertex : Base : Base
1 : 4 : 4 A C

11. B Ratio Vertex : Base : Base 1 : 4 : 4 1x + 4x + 4x = 180 9x = 180
In an isosceles triangle, if the ratio of the vertex angle to the base angle is 1:4, what is the degree measure of the base angle? 7 B
Ratio
Vertex : Base : Base
1 : 4 : 4
1x + 4x + 4x = 180
9x = 180
x = 20
A = 4(20) = 80 A C

12. 8
The unequal sides of a triangle are integers. If the size order is 5, x, and 15, what is the largest possible value of x?
Triangle Side Lengths
5, 6, 15
5, 10, 15
5, 13, 15
5, 7, 15
5, 11, 15
5, 14, 15
5, 8, 15
5, 12, 15
5, 15, 15
5, 9, 15
The middle side can not
be equal to 15.
Answer is 14

13. In the right triangle ABC, segment DE is drawn from side to as shown, forming right triangle ADE. If is 24,
is 12, and is 4, what is the length of ? 9 8 12
12  x = 24  8 x
12x = 192 4
x = 16 24

14. In the figure, the lengths of , , and
are equal. x + w = 10
All sides
equal
Equilateral
Triangle
All angles
equal
Supplementary Angles
(Sum of angles 180°)
60°
x = 180 – 60 = 120
w = 180 – 60 = 120
x + w
= = 240
60°
60°

15. A C = 180° – 80° – 50° = 50° 80° AB = AC 2x – 12 = x – 3 –x –x
In ABC, the measure of A is 80° and the measure of B is 50°. If the length of
AB is 2x – 12 and the length of AC is x – 3, what is the length of AB? 11 A
C = 180° – 80° – 50°
= 50°
80°
AB = AC
2x – 12 = x – 3 –x –x
x – 12 = –3
50°
50°
x = 9 B C
AB = 2(9)–12
= 18 –12
= 6

16. 12
In the figure, AB = BC = CA. What is the length of , if bisects ABC?
Method #1
Use Pythagorean Theorem
to find length of
a2 + b2 = c2
? = 42 ?
?2 + 4 = 16
?2 = 12 2

17. 12
In the figure, AB = BC = CA. What is the length of , if bisects ABC?
Method #2
60°
Use 30° – 60° – 90°
Right Triangle Rule
30°
60° x 2x
30° ?
60°
60° 2

18. x = 5x = 5(8) = 40 In the figure, what is the length of ? 2x 24 3x 45°13
In the figure, what is the length of ?
Use 45° – 45° – 90°
Right Triangle Rule
45° x 2x 24 3x
45°
Find length of
= 5x
3x = 24
x = 8
= 5(8)
= 40

19. 14
In the isosceles right triangle ABC, leg equals 6. What is the length of ?
3x = 6
x = 2 6
= 5x
= 5(2)
= 10

20. 15
In the figure, if ABC is an isosceles triangle, what is the length of ?
Part 1
Find unknown
sides of ∆ACD
Use 30° – 60° – 90°
Right Triangle Rule
30°
60° x 2x
60° 5
ADC = 180 - 90 - 30
ADC = 60

21. 15
In the figure, if ABC is an isosceles triangle, what is the length of ?
Part 2
Use ∆ABC to find length of
Note: ∆ABC is isosceles. ? 5

22. In the right ABC, the length of leg is 16
In the right ABC, the length of leg is
and D is the midpoint of Find the length of x=
= 3
30°
C = 180° – A – B
= 180° – 60° – 90°
= 30°

23. 17
In the figure, x = 60°, y = 60°, z = 30° and the length of is 2. What is the length of ?
B = 90
A = 60 2
30°
C = 180 – 90 – 60
C = 30 2
60°
30°
60°
60°

24. In the figure, ABC is a right isosceles triangle with
In the figure, ABC is a right isosceles triangle with If AD = 2, what is the length of ? 18
a2 + b2 = c2 x
x2 + x2 = 22
2x2 = 4 x
x2 = 2

25. 19

26. 19 13 12 5

27. 20
Find the tangent of K.

28. Find the tangent of K. a2 + b2 = c2 x2 + 242 = 512 x2 + 576 = 260120
Find the tangent of K.
a2 + b2 = c2
x = 512
x = 2601
–576
–576
x = 2025
x = 45 x 45

29. 21

30. 22
cos  = ?

31. 23

32. 24
Find the length of JK. L
34.6 mm
18 K J
1  x =  34.6 x
x =
cos 18 = .9511

33. 25
Find the length of FH.

34. tan 31 = .60 Find the length of FH. x 1  x = 10  0.60 x = 6.0 H G F25
Find the length of FH. H x
31 G F
10 in.
1  x = 10  0.60
x = 6.0
tan 31 = .60