Foundations for Geometry

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Foundations for Geometry

Section 1.1 A Entrance Quiz

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Refer to the figure for Exercises 1 and 2.

1. Which represents the name of the ray whose endpoint is K and that passes through R?

A C

B D

2. In the diagram, how many different rays have endpoint R?

F 1 H 3

G 2 J 4

Refer to the figure for Exercises 3 and 4.

3. Which line contains points S and U?

A line m C line p

B line n D

4. In the diagram, how many different segments can be named?

F 0 H 2

G 1 J 3

Refer to the figure for Exercises 5 and 6.

5. What is MP?

A 1 C 4

B 2 D 5

6. What is LP?

F -7.5 H 2.5

G -2.5 J 7.5

7. Write below, in your own words, the description of a point, line, and plane.

Holt McDougal Geometry

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Holt McDougal Geometry

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Foundations for Geometry

Section B Quiz

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1. What is the perimeter of a rectangle whose width is (x - 7) units and whose length is (3x + 10) units?

A (2x + 17) units C (4x + 34) units

B (4x + 3) units D (8x + 6) units

2. To the nearest whole number, what is the area of this circle?

F 1,810 in2 H 113 in2

G 452 in2 J 38 in2

3. To the nearest tenth, what is the circumference of a circle whose
diameter is 8 meters?

A 201.1 m C 25.1 m

B 50.2 m D 12.6 m

4. Find the coordinates for the midpoint
of with endpoints M(-3, 8) and
N(-7, 6).

F (-5, 7) H (2, 1)

G (5, -7) J (-2, -1)

5. K is the midpoint of , P has coordinates (-9, -4), and K
has coordinates (-1, 6). What
are the coordinates of Q?

A (-5, 1) C (-11, 8)

B (5, 10) D (7, 16)

6. What is the distance, to the nearest
whole number, from K(5, 6) to P(1, -4)?

F 14 H 11

G 13 J 6

7. Which best describes the transformation?

A preimage C rotation

B reflection D translation

8. A figure has vertices at K(5, 5),
L(5, 3), M(1, 1), and N(3, 5). After a transformation, the image of the figure has vertices at K'(-5, -5), L'(-3, -5), M'(-1, -1), and N'(-5, -3). Which best describes the transformation?

F preimage H rotation

G reflection J translation

Holt McDougal Geometry

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Geometric Reasoning

Section A Quiz

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1. What is the next letter in the sequence?
D, H, L, P, . . .

A Q C S

B R D T

2. Which is the counterexample that proves the conjecture false?

“If two rays have the same endpoint, then they are opposite rays.”

F H

G J

3. Identify the hypothesis of the conditional statement “Two angles are complementary if the sum of their measures is 90 degrees.”

A if

B Two angles are complementary

C the sum of their measures is
90 degrees

D Two angles are complementary if the sum of their measures is 90 degrees.

4. Which conditional statement has the same truth value as this statement?
“The sum of two odd numbers is even.”

F If two even numbers are added, then their sum is even.

G If an even and odd number are added, then their sum is even.

H If two even numbers are multiplied, then their product is odd.

J If two odd numbers are multiplied, then their product is even.

5. What is the inverse of the statement
“If two coplanar lines do not intersect, then they are parallel”?

A If two coplanar lines do not intersect, then they are not parallel.

B If two coplanar lines intersect, then they are not parallel.

C If two lines are parallel, then they are coplanar and do not intersect.

D If two coplanar lines are not parallel, then they intersect.

6. Which conjecture is valid by the Law of Syllogism for the following scenario?
“If Joe buys Nancy a card, he will give it to her. If Nancy is having a birthday, then Joe will buy her a card.”

F If Nancy is having a birthday, then Joe will give her a card.

G If Joe buys Nancy a card, then she
is having a birthday.

H If Joe gives Nancy a card, then he bought the card.

J If Joe gives Nancy a card, then she
is having a birthday.

7. Consider the related biconditional statement for the conditional statement “If Shelly lives in Texas, then she lives in the United States.”

Which of the following statements is true about the related biconditional statement?

A The biconditional is true because the conditional is true.

B The biconditional is false because the conditional and its converse are false.

C The biconditional is true because the conditional and its converse are true.

D The biconditional is false because the converse of the conditional is false.

Holt McDougal Geometry

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Geometric Reasoning

Section B Quiz

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1. If r + 14 = -9, what justifies r = -23?

A Transitive Property of Equality

B Subtraction Property of Equality

C Symmetric Property of Equality

D Reflexive Property of Equality

2. If = 8, what justifies x - 1 = 16?

F Subtraction Property of Equality

G Division Property of Equality

H Transitive Property of Equality

J Multiplication Property of Equality

3. If 5 = 2k, what justifies 2k = 5?

A Multiplication Property of Equality

B Division Property of Equality

C Symmetric Property of Equality

D Reflexive Property of Equality

4. Which completes the statement?
If 2a(a - 4) = 10, then ______by
the Distributive Property.

F 2a(a - 4) - 10 = 0

G a = 5 or -1

H a(a - 4) = 5

J 2a2 - 8a = 10

5. Which completes the statement?
If 6x = 5 and d = 6x, then ______by
the Transitive Property of Equality.

A d = 5 C 6x = d

B x = D x =

6. Which completes the statement?
If then ______by the Symmetric Property of Congruence.

F RS = GH H

G J

7. Given: L bisects ; M bisects

Prove: KL = MN

Proof:
Since L bisects and M bisects by definition of bisect, and
Then, by the ?,
Finally, KL = MN by the definition of congruent segments.
Which completes the proof?

A Common Segments Theorem

B Transitive Property of Congruence

C Segment Addition Postulate

D Symmetric Property of Congruence

8. Given: Ð1 @ Ð4

Prove: Ð2 @ Ð3

Proof:

Statements / Reasons
1. Ð1 @ Ð4 / 1. Given
2. Ð1 and Ð2 are supp.,
and Ð3 and Ð4 are
supp. / 2. Lin. Pairs
Thm.
3. Ð2 @ Ð3 / 3. ?

Which completes the proof?

F Transitive Property of Congruence

G Vertical Angles Theorem

H Congruent Supplements Theorem

J Angle Addition Postulate

9. For the following statement, what is the “Prove” statement?
If ABCD is a rhombus, then it is a parallelogram.

A ABCD is a quadrilateral.

B ABCD is a rhombus.

C ABCD is a parallelogram.

D ABCD is not a square.

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Parallel and Perpendicular Lines

Section A Quiz

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Refer to the figure for Exercises 1–3.

1. Which segment is perpendicular to ?

A C

B D

2. Which segment is parallel to ?

F H

G J

3. Which segment is NOT skew to ?

A C

B D

Refer to the figure for Exercises 4 and 5.

4. Which pair of angles are corresponding angles?

F Ð1 and Ð4 H Ð2 and Ð5

G Ð6 and Ð8 J Ð8 and Ð7

5. Which pair of angles are alternate exterior angles?

A Ð4 and Ð8 C Ð3 and Ð7

B Ð2 and Ð5 D Ð1 and Ð4

6. What is the value of x?

F 35 H 15

G 20 J 12.5

7. Which could you use to show that u || v?

A Ð1 and Ð8 are supplementary.

B Ð4 and Ð8 are supplementary.

C Ð3 and Ð7 are congruent.

D Ð7 and Ð8 are congruent.

8. Why is m ^ n?

F If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

G If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary.

H In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

J If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular.

Holt McDougal Geometry

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Holt McDougal Geometry

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Parallel and Perpendicular Lines

Section B Quiz

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1. What is the slope of the line that passes through (4, 0) and (8, -1)?

A -4 C -12

B D

2. What is the slope of the line that passes through (-6, -4) and (9, -19)?

F H -1

G J -5

3. The slope of a line is . What is the slope of a line that is perpendicular to it?

A C

B D

4. What is the slope of a line parallel to the line that passes through (4, -3) and
(3, -1)?

F H

G 2 J -2

5. Which is the equation for the line having slope -6 that passes through (5, -5)?

A y = -6x

B y = -6x - 5

C y + 5 = -6(x - 5)

D y + 5 = -6(x + 5)

6. Which is the equation for the line that passes through (-4, -3) and (-2, 3)?

F y = 3x + 15 H y = -3x - 15

G y = 3x + 9 J y = -3x - 9

7. Which is the graph of y - 1 = -2(x + 3)?

A C

B D

8. Which equation represents the graph of the line that coincides with the graph of
?

F 6x + 4y = 36 H

G y - 3 = -9(x + 2) J 2x - 3y = 9

9. The graph of which line intersects the graph of y + 10 = -5(x - 1) in only one point?

A y + 10 = 5(x - 1)

B y = -5(x – 2)

C 5x + y = -5

D y = 5(-x + 5)

10. The graph of which
equation is parallel
to the line in the
graph?

F 3x - y = 2

G y - 1 = -3(x - 1)

H y = 3x

J y = -2x + 3

Holt McDougal Geometry

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Holt McDougal Geometry

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Holt McDougal Geometry

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Triangle Congruence

Section A Quiz

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1. The polygon Q(3, 2), R(6, 5), S(6, 2) undergoes the transformation:
(x, y) ® (4x, 4y). Name the coordinates
of the image points.

A Q'(3, 2), R'(6, 5), S'(6, 2)

B Q'(7, 6), R'(10, 9), S'(10, 6)

C Q'(12, 8), R'(24, 20), S'(24, 8)

D Q'(–1, –2), R'(2, 1), S'(2, –2)

2. The angles of a triangle measure 4°,
86°, and 90°. Which classification of
the triangle is correct?