Download GEOMETRY TOPIC 4 Line and Angle Relationships Good Luck To

GEOMETRY
TOPIC 4 Line and Angle Relationships
Good Luck To ____________________________________________________
Period ________________
Date __________________________ DIRECTIONS: Answer each question and show all work in the space provided.
1. Name a pair of corresponding angles.
2
1
4
3
5
6
7
A. ∠ 1 and ∠ 4
B. ∠ 1 and ∠ 5
8
C. ∠ 2 and ∠ 7
D. ∠ 2 and ∠ 4
2. The segment connecting the vertex of a triangle to the midpoint of its opposite
side is a(n) ____________
A. altitude
B. angle bisector
C. median
D. midsegment
3. In the figure below, what type of angles are ∠ 3 and ∠ 6?
2
1
3
4
5
6
7
8
A. alternate exterior angles
B. alternate interior angles
C. linear pair of angles
D. vertical angles
Page 1 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
In the figure below, calculate the measure of ∠ 1 and the measure of ∠ 2.
(Problems 4 and 5)
162°
1
2
4. m ∠ 1 = _____
5. m ∠ 2 = _____
6. A flag poll lies perpendicular to a hill and makes a 50° angle as shown below.
What is the measure of ∠ 1?
50°
1
Hill
m ∠ 1 = _____
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GEOMETRY
TOPIC 4 Line and Angle Relationships
7. In quadrilateral HIJK, as shown below, HI II KJ . If the measure of ∠ H is 62°.
What is the measure of ∠ K?
I
H
62°
J
K
m ∠ K = _____
8. In the figure below, lines m and n are parallel and are cut by transversal t. What is
the value of x?
m
n
t
74°
(4x + 22)°
The value of x is _____
Page 3 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
9. If p II s, then what is the value of x.
(8x + 17)°
(3x+9)°
p
s
The value of x is __________
10. If x = 14, is p II q? Explain your reasoning.
p
q
75°
7x - (2x - 5)
Page 4 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
Use the figure below for problems 11 -16
Given l ll m. Calculate the measure of each lettered angle.
120°
f
b
a
l
e
c
d
m
11. a: _________
12. b: _________
13. c: _________
14. d: _________
15. e: _________
16. f: __________
Page 5 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
17.
BD bisects ∠ABC , m∠ABC = 68° , and m∠BDC = 88° What is
the m∠A ?
A
D
B
C
m∠A : ______________ 18. Find the coordinate for midpoint C.
Coordinate for point C ______________________
19.
suur
AB passes through points A(3, 6), B(-4, 1) and
coordinates of point D if
suur
CD
suur suur
AB || C D
. Find the
passes through C(-5, -3).
Coordinates of D ______________
Page 6 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
20. Given points M(0, 7), N(-5, 2), and O(-4, -2), find the coordinate of point Q such
that
suuur
MN
and
suur
OQ
are perpendicular. Coordinates of Q _______________
21. Use a compass and a straight edge to construct the angle bisector through the
given angle below.
22. Use a compass and a straight edge to construct the perpendicular bisector
through the given line segment.
Page 7 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
uuur
23. If BE bisects ∠ABD , find m ∠ABE ∠ABE = _____ 24. Complete the following statement: Point F is equidistant from _______________ C
G
B
F
D
I
J
A
H
E
25. A revolving sprinkler needs to be set up to water every part of a triangular garden. Where should the sprinkler be located so that it reaches the entire garden but doesn’t spray farther than necessary? The sprinkler should be located ___________________________________________. Page 8 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
26. Name the geometric construction 27. Name the geometric construction 28. Name the geometric construction For Problems 29 – 35: Identify each statement as True (A) or False (B). 29. The circumcenter of a triangle is the center of gravity of the triangular region. 30. In a triangle, an altitude is shorter than either side from the vertex 31. The circumcenter is the intersection of the perpendicular bisectors of the sides of a triangle. 32. The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line. 33. The incenter is equally distant from the three sides of a triangle. 34. In a triangle, if the perpendicular bisector of a side and an altitude coincide, then the triangle is isosceles. 35. The centroid is the intersection of the three medians of a triangle. Page 9 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
ANSWER KEY
Problem
Number
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
Answer
B.
and
C. median
B. alternate interior angles
18°
162°
140°
118°
21
14
Yes, since the alternate exterior angles are congruent, then
.
a. 60°
b. 60°
c. 60°
d. 60°
e. 60°
f. 120°
54°
MA.912.G.1.3
MA.912.G.4.2
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
Answers may vary, sample answers: (2 , 2)or(0,4/7)or(-12,-8)
Answers may vary, sample answers: (-3. -3)or(0,-6)or(-8,2)
MA.912.G.1.2
MA.912.G.1.2
MA.912.G.8.6
22.
23.
24.
25.
26.
27.
Standard
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.1.3
MA.912.G.4.2
MA.912.G.1.1
MA.912.G.8.6
50o
Point B and Point C; a point on the perpendicular bisector is
equidistant from the endpoints of the segment
Circumcenter
Angle Bisector Construction
Parallel Line Construction
MA.912.G.2.3
MA.912.G.4.2
MA.912.G.2.3
MA.912.G.2.3
MA.912.G.2.3
Page 10 of 11
GEOMETRY
TOPIC 4 Line and Angle Relationships
ANSWER KEY
Problem
Number
28.
29.
30.
31.
32.
33.
34.
35.
Answer
Equilateral Triangle Construction
B. False – the centroid is the center of gravity
B.False – the triangle could be a right triangle
A. True
A. True
A. True
B. False – this is also true in an equilateral triangle
A. True
Standard
MA.912.G.2.3
MA.912.G.4.2
MA.912.G.4.2
MA.912.G.4.2
MA.912.G.4.2
MA.912.G.4.2
MA.912.G.4.2
MA.912.G.4.2
Page 11 of 11