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
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