Download Fill in the blank in each sentence with the vocabulary term that best

6. Give another name for line b.
SOLUTION: There are two point S and T marked on the line b.
So, the line b can also be called Study Guide and Review
Fill in the blank in each sentence with the
vocabulary term that best completes the
sentence.
1. A _____ is a flat surface made up of points that
extends infinitely in all directions.
SOLUTION: A plane is a flat surface made up of points that
extends infinitely in all directions. Therefore, the
correct answer is plane.
7. Name a point that is not contained in any of the three
lines a, b, or c.
SOLUTION: Here, W is a point on the plane R and is not on any of
the lines on the plane.
8. Give another name for plane WPX.
SOLUTION: The plane WPX is also named as plane R.
2. A set of points that all lie on the same line are said to
be _____.
Name the geometric term that is best modeled
by each item.
SOLUTION: A set of points that all lie on the same line are said to
be collinear points. Therefore, the correct answer is
collinear.
9. 3. If two lines intersect to form four right angles, the
lines are called _____.
SOLUTION: In the figure, two flat surfaces intersect each other.
The two flat surfaces model two planes. Since the
intersection of two planes form a line, the item
models a line.
SOLUTION: If two lines intersect to form four right angles, the
lines are called perpendicular.
4. If the sum of the measures of two angles is 180, then
the angles are called _____ angles.
SOLUTION: If the sum of the measures of two angles is 180, then
the angles are called supplementary angles.
Use the figure to complete each of the
following.
10. SOLUTION: Each bead denotes a location. So, it models a point.
Find the value of the variable and XP, if X is
between P and Q.
11. XQ = 13, XP = 5x – 3, PQ = 40
5. Name the intersection of lines a and c.
SOLUTION: The lines a and c intersect at the point P.
6. Give another name for line b.
SOLUTION: There are two point S and T marked on the line b.
So, the line b can also be called 7. Name a point that is not contained in any of the three
lines a, b, or c.
SOLUTION: eSolutions
Manual
by the
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Here,
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point on
plane R and is not on any of
the lines on the plane.
SOLUTION: Here X is between P and Q. So, PQ = XP + XQ.
We have XQ = 13, XP = 5x – 3, and PQ = 40.
40 = 13 + 5x – 3
30 = 5x
6=x
So, XP = 5(6) – 3 = 27.
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12. XQ = 3k, XP = 7k – 2, PQ = 6k + 16
SOLUTION: 10. SOLUTION: Study
Guide and Review
Each bead denotes a location. So, it models a point.
Find the value of the variable and XP, if X is
between P and Q.
11. XQ = 13, XP = 5x – 3, PQ = 40
The distance between points A and B is
.
14. P(2, –1) and Q(10, –7)
SOLUTION: SOLUTION: Here X is between P and Q. So, PQ = XP + XQ.
We have XQ = 13, XP = 5x – 3, and PQ = 40.
The distance between P and Q is
40 = 13 + 5x – 3
30 = 5x
6=x
or 10. 15. M(9, –2) and N(–1, 4)
SOLUTION: So, XP = 5(6) – 3 = 27.
12. XQ = 3k, XP = 7k – 2, PQ = 6k + 16
SOLUTION: Here X is between P and Q. So, PQ = XP + XQ.
We have XQ = 3k, XP = 7k – 2, PQ = 6k + 16.
The distance between points M and N is
.
16. J(3, 2) and K(6, –5)
SOLUTION: 6k + 16 = 7k – 2 + 3k
6k – 10k = –2 – 16
–4k = –18
k = 4.5
So, XP = 7(4.5) – 2 = 29.5.
Find the distance between each pair of points.
13. A(–3, 1) and B(7, 13)
SOLUTION: The distance between J and K is
.
Find the coordinates of the midpoint of a
segment with the given endpoints.
18. L(–3, 16), M (17, 4)
SOLUTION: Use the Midpoint Formula
.
The distance between points A and B is
.
14. P(2, –1) and Q(10, –7)
SOLUTION: Substitute.
The midpoint of
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is (7, 10).
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19. C(32, –1), D(0, –12)
Guide and Review
Study
The distance between J and K is
.
Find the coordinates of the midpoint of a
segment with the given endpoints.
18. L(–3, 16), M (17, 4)
SOLUTION: Use the Midpoint Formula
The midpoint of
is (16, –6.5).
Find the coordinates of the missing endpoint if
M is the midpoint of
20. X(–11, –6), M (15, 4)
SOLUTION: Let the coordinates of Y be (x, y).
.
Then by the Midpoint Formula,
.
Substitute.
Write two equations to find the coordinates of Y.
The midpoint of
is (7, 10).
19. C(32, –1), D(0, –12)
SOLUTION: Use the Midpoint Formula
. Substitute.
The coordinates of Y are (41, 14).
21. M (–4, 8), Y(19, 0)
The midpoint of
is (16, –6.5).
Find the coordinates of the missing endpoint if
M is the midpoint of
20. X(–11, –6), M (15, 4)
SOLUTION: Let the coordinates of Y be (x, y).
SOLUTION: Let the coordinates of X be (x, y).
Then by the Midpoint Formula,
.
Write two equations to find the coordinates of X.
Then by the Midpoint Formula,
.
Write two equations to find the coordinates of Y.
The coordinates of X are (–27, 16).
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The coordinates of Y are (41, 14).
For Exercises 25–28, refer to the figure below.
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SOLUTION: Vertical angles are two nonadjacent angles formed
by two intersecting lines. Here, QWP and XWV
are a pair of vertically opposite angles.
Study Guide and Review
The coordinates of X are (–27, 16).
For Exercises 25–28, refer to the figure below.
32. If m SXW = 5x – 16, find the value of x so that
SOLUTION: Since
25. Name the vertex of
That is, 5x – 16 = 90.
Add 16 to both sides.
5x = 106
Divide both sides by 5.
x = 21.2
7.
SOLUTION: Here, 7 is same as the angle CGJ. So, the vertex
of the angle is G.
26. Write another name for
SOLUTION: Here, 4 is same as the
Name each polygon by its number of sides.
Then classify it as convex or concave and
regular or irregular.
4.
CDG.
34. 27. Name the sides of
2.
SOLUTION: Here, 2 is same as the
sides are
SOLUTION: The polygon has 3 sides. So, it is a triangle. No line
containing any of the sides will pass through the
interior of the triangle, so it is convex. All of the sides
are congruent, so it is equilateral. All of the angles
are congruent, so it is equiangular. Since the polygon
is convex, equilateral, and equiangular, it is regular.
So this is a regular triangle.
ACH. Therefore, its
For Exercises 30–32, refer to the figure below.
30. Name an angle supplementary to
TVY.
SOLUTION: Supplementary angles are two angles with measures
that have a sum of 180°. Here, TVR is
supplementary to TVY.
35. SOLUTION: The polygon has 12 sides. So, it is a dodecahedron.
Four of the lines containing the sides of the polygon
will pass through the interior of the dodecahedron, so
it is concave.
31. Name a pair of vertical angles with vertex W.
SOLUTION: Vertical angles are two nonadjacent angles formed
by two intersecting lines. Here, QWP and XWV
are a pair of vertically opposite angles.
32. If m SXW = 5x – 16, find the value of x so that
SOLUTION: Since
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That is, 5x – 16 = 90.
Add 16 to both sides.
Only convex polygons can be regular, so this is an
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irregular dodecahedron.
interior of the triangle, so it is convex. All of the sides
are congruent, so it is equilateral. All of the angles
are congruent, so it is equiangular. Since the polygon
is convex, equilateral, and equiangular, it is regular.
Study
Review
SoGuide
this is and
a regular
triangle.
35. SOLUTION: The polygon has 12 sides. So, it is a dodecahedron.
Four of the lines containing the sides of the polygon
will pass through the interior of the dodecahedron, so
it is concave.
Only convex polygons can be regular, so this is an
irregular dodecahedron.
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