Download 10Math_GEOM_L_01

Five-Minute Check (over Lesson 1–4)
Then/Now
New Vocabulary
Key Concept: Special Angle Pairs
Example 1: Real-World Example: Identify Angle Pairs
Key Concept: Angle Pair Relationships
Example 2: Angle Measure
Key Concept: Perpendicular Lines
Example 3: Perpendicular Lines
Key Concept: Interpreting Diagrams
Example 4: Interpret Figures
Over Lesson 1–4
Refer to the figure.
Name the vertex of 3.
C. C
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B
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A
D. D
A.
B.
C.
D.
A
B
C
D
D
B. B
C
A. A
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Over Lesson 1–4
Refer to the figure. Name
a point in the interior of
ACB.
C. B
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B
D. A
A
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A.
B.
C.
D.
A
B
C
D
D
B. D
C
A. G
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Over Lesson 1–4
Refer to the figure. Which
ray is a side of BAC?
A. DB
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B
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A
D. BC
A
B
C
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D
D
C. BD
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B.
C.
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D.
C
B. AC
Over Lesson 1–4
Refer to the figure. Name
an angle with vertex B that
appears to be acute.
A. ABG
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B
D. BDC
A
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A
B
C
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D
D
C. ADB
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B.
C.
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D.
C
B. ABC
Over Lesson 1–4
Refer to the figure. If
bisects
ABC, mABD = 2x + 3, and
mDBC = 3x – 13, find mABD.
C. 29
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B
A
D. 23
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A
B
C
D
D
B. 35
A.
B.
C.
D.
C
A. 41
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Over Lesson 1–4
OP bisects MON and mMOP = 40°. Find the
measure of MON.
A. 20°
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B
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A
D. 80°
A
B
C
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D
D
C. 60°
A.
B.
C.
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D.
C
B. 40°
You measured and classified angles.
(Lesson 1–4)
• Identify and use special pairs of angles.
• Identify perpendicular lines.
• adjacent angles
• linear pair
• vertical angles
• complementary angles
• supplementary angles
• perpendicular
Identify Angle Pairs
A. ROADWAYS Name an
angle pair that satisfies the
condition two angles that
form a linear pair.
A linear pair is a pair of adjacent angles whose
noncommon sides are opposite rays.
Sample Answers: PIQ and QIS, PIT and
TIS, QIU and UIT
Identify Angle Pairs
B. ROADWAYS Name an
angle pair that satisfies the
condition two acute vertical
angles.
Sample Answers: PIU and RIS, PIQ and
TIS, QIR and TIU
A. Name two adjacent angles
whose sum is less than 90.
A. CAD and DAE
B. FAE and FAN
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A
B
C
D
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D
A
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C
D. BAD and DAC
B
C. CAB and NAB
A.
B.
C.
D.
B. Name two acute vertical angles.
A. BAN and EAD
B. BAD and BAN
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0%
A
B
C
D
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D
A
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C
D. FAN and DAC
B
C. BAC and CAE
A.
B.
C.
D.
Angle Measure
ALGEBRA Find the measures of two supplementary
angles if the measure of one angle is 6 less than five
times the measure of the other angle.
Understand The problem relates the measures of two
supplementary angles. You know that the
sum of the measures of supplementary
angles is 180.
Plan
Draw two figures to represent the angles.
Angle Measure
Solve
6x – 6 = 180
6x = 186
x = 31
Simplify.
Add 6 to each side.
Divide each side by 6.
Angle Measure
Use the value of x to find each angle measure.
mA = x
= 31
Check
mB = 5x – 6
= 5(31) – 6 or 149
Add the angle measures to verify that the
angles are supplementary.
mA + mB = 180
31 + 149 = 180
180 = 180 
Answer: mA = 31, mB = 149
ALGEBRA Find the measures of two complementary
angles if one angle measures six degrees less than
five times the measure of the other.
A. 1°, 1°
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B
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A
D. 14°, 76°
A
B
C
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D
D
C. 16°, 74°
A.
B.
C.
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D.
C
B. 21°, 111°
Perpendicular Lines
ALGEBRA Find x and y so that
KO and HM are perpendicular.
Perpendicular Lines
90 = (3x + 6) + 9x
Substitution
90 = 12x + 6
Combine like terms.
84 = 12x
Subtract 6 from each side.
7 =x
Divide each side by 12.
Perpendicular Lines
To find y, use mMJO.
mMJO = 3y + 6
Given
90 = 3y + 6
Substitution
84 = 3y
Subtract 6 from each side.
28 = y
Divide each side by 3.
Answer: x = 7 and y = 28
A. x = 5
B. x = 10
C. x = 15
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D
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C
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B
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A
D. x = 20
A.
B.
C.
D.
A
B
C
D
Interpret Figures
A. Determine whether the following statement can
be justified from the figure below. Explain.
mVYT = 90
Interpret Figures
B. Determine whether the following statement can
be justified from the figure below. Explain.
TYW and TYU are supplementary.
Answer: Yes, they form a
linear pair of angles.
Interpret Figures
C. Determine whether the following statement can
be justified from the figure below. Explain.
VYW and TYS are adjacent angles.
Answer: No, they do not
share a common
side.
A. Determine whether the
statement mXAY = 90 can
be assumed from the figure.
A. yes
B. no
A. A
B. B
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B
A
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B. Determine whether the
statement TAU is
complementary to UAY
can be assumed from the
figure.
A. yes
A. A
B. B
B. no
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B
A
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C. Determine whether the
statement UAX is
adjacent to UXA can be
assumed from the figure.
A. yes
A. A
B. B
B. no
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B
A
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