Practice QuizTriangles

60QPX

1 If PRQ is an isosceles triangle with PQ = PR, find the measure of QPX.

3030QPX

30

?

QPX: Exterior Angle

60

∆PRQ: Isosceles TriangleThe base angles are equal.

2 In the figure, if ABC is the same size and shape as ABD, then the degree measure of BAD =

70

7040180EBC

70EBC

35 35 7035180BAC

75BAC

75 75BAD ?75

3

115

In the figure, if side RS = ST and x = 115°, what is the measure of angle w?

IsoscelesTriangle

BaseAngles

A = B

A B

3

115

In the figure, if side RS = ST and x = 115°, what is the measure of angle w?

115

115

T = 115Supplementary Angles

of base angles are equal.

BaseAngles

A = B

A Bw and T are

Vertical Angles

4 In the figure, if x = 2z and y = 70, what is the value of z?

2z

70

2z = 70 + z– z – z

z = 70

Exterior AnglesRule

5 In the figure, if side AB = AC andw = 145°, what is the measure of x?

?

? = 180° – 145°145°

? = 35°

5 In the figure, if side AB = AC andw = 145°, what is the measure of x?

35°

x = 35° + 35°

145°35°

x = 70°Exterior Angles

Rule

IsoscelesTriangle

6 If the ratio of the angles of a triangle is 2:3:4, what is the degree measure of the largest angle?

180432 xxx

1809 x

9

180

9

9

x

20x

Largest Angle

4x4(20) = 80

7 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?

B

A C

Vertex Angle: BBase Angle: A

Base Angle: C

RatioVertex : Base : Base

1 : 4 : 4

7 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?

B

A C

RatioVertex : Base : Base

1 : 4 : 4

1x + 4x + 4x = 1809x = 180x = 20

A = 4(20) = 80

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

The middle side can not be equal to 15.

Answer is 14

5, 6, 15

5, 7, 15

5, 8, 15

5, 9, 15

5, 10, 15

5, 11, 15

5, 12, 15

5, 13, 15

5, 14, 15

5, 15, 15

9 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 ?

AB

BC

AB

AC

BDDE

24

12

4x

8

12 x = 24 812x = 192

x = 16

12

24

8

x

10 In the figure, the lengths of , , and are equal. x + w =

AB BCCA

All sidesequal

EquilateralTriangle

All anglesequal

60°

60° 60°

Supplementary Angles(Sum of angles 180°)

x = 180 – 60 = 120w = 180 – 60 = 120

x + w = 120+120 = 240

11 In ABC, the measure of A is 80° and the measure of B is 50°. If the length ofAB is 2x – 12 and the length of AC is x – 3, what is the length of AB?

B

A

C

80°

50° 50°

C = 180° – 80° – 50° = 50°

AB = AC2x – 12 = x – 3–x –x

x – 12 = –3x = 9

AB = 2(9)–12 = 18 –12 = 6

12 In the figure, AB = BC = CA. What is

the length of , if bisects ABC?

2

BD BDUse Pythagorean Theoremto find length of .BD

?

a2 + b2 = c2

?2 + 22 = 42

?2 + 4 = 16?2 = 12

2 12?

Method#1

? 2 3

12 In the figure, AB = BC = CA. What is

the length of , if bisects ABC?

2

BD BD

?

60° 60°

30°

60° Use 30° – 60° – 90°Right Triangle Rule

3x

30°

60°x

2x

? 2 3

Method#2

13

In the figure, what is the length of ?BD

2x

3x

224

Use 45° – 45° – 90°Right Triangle Rule

45°

45°

x

x

2x

Find length of AC

242

224AC

24

45°

3x = 24x = 8

xxBD 32 = 5x= 5(8) = 40

ACBC

14 In the isosceles right triangle ABC, leg equals 6. What is the length of ?

ACBD

6

3x = 6x = 2

ACBC

xxBD 32 = 5x= 5(2) = 10

15

In the figure, if ABC is an isosceles triangle, what is the length of ? DB

60°

Part 1Find unknownsides of ∆ACD

5

5 3

Use 30° – 60° – 90°Right Triangle Rule

3x

30°

60°x

2x

ADC = 180 - 90 - 30ADC = 60

15

In the figure, if ABC is an isosceles triangle, what is the length of ? DB

5

5 3

Part 2Use ∆ABC to find length of .DB

5 3

CB CD DB

5 3 5

Note: ∆ABC is isosceles.

AC BC?

16 In the right ABC, the length of leg is and D is the midpoint of . Find the length of .

AB3 AC

BC

3

C = 180° – A – B

= 180° – 60° – 90° = 30°

30°

x=3x 3 3

9 = 3

17

In the figure, x = 60°, y = 60°, z = 30° and the length of is 2. What is the length of ?BD CD

60°

60° 60°30°

A = 60

B = 90

C = 180 – 90 – 60C = 30

30°

2BD CD 2

2

18 In the figure, ABC is a right isosceles triangle with . If AD = 2, what is the length of ?

DE AB

AE

2

45

45

x

x

a2 + b2 = c2

x2 + x2 = 22

2x2 = 4

x2 = 22 2x

2x

2AE

19

Asin

Acos

Atan

38.013

5

92.013

12

42.012

5

19

Bsin

Bcos

Btan

38.013

5

92.013

12

4.25

12

1312

5

20 Find the tangent of K.

20 Find the tangent of K.

a2 + b2 = c2

x2 + 242 = 512

x

x2 + 576 = 2601–576 –576

x2 = 20252 2025x

x = 4545

24 8tan

45 15K

21

222 cba

2

3

PQ

QR

2 3

x

222 32 x

942 x5 2 x

5 2 x

5 x

5

5

2tan

tan ?

22

222 cba

2

3

PQ

QR

2 3

x

222 32 x

942 x5 2 x

5 2 x

5 x

5

cos = ?

5cos

3

23

222 cba 222 85 x

64252 x93 2 x

93 2 x

93 x

5cos

8A

5

8x93

78.08

39sin A

sin ?A

24

Find the length of JK.

K

L

J18

x

cos 18 = .9511

34.6 mm

cos1834.6

x

.951134.6

x

.9511

34.6 1

x

1 x = .9511 34.6

x = 32.91

25 Find the length of FH.

.60

10 1

x

25 Find the length of FH.

F

H

G31

10 in.

x

tan 31 = .60

tan 3110

x

1 x = 10 0.60

x = 6.0

.6010

x