Quiz about Proving and Using Geometric Properties

Question 1

What is the missing step in constructing a perpendicular bisector of a line segment?

Accepted Answer

Without changing the compasses' width, draw an arc above and below the line.

Answer

Without changing the compasses' width, draw an arc only above the line.

Answer

Without changing the compasses' width, draw an arc only below the line.

Question 2

Which is the geometric mean for this triangle?

Accepted Answer

$$BD^2=AD\cdot BC$$

Answer

$$AD=BD*DC$$

Answer

$$BD=AD\cdot BC$$

Answer

$$BC=AD*BD$$

Question 3

See diagram

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 4

How can you prove step #2?

Accepted Answer

Vertical angle theorem

Answer

Subtraction property of equality

Answer

Transitive property of congruence

Answer

Definition of supplementary angles

Question 5

What is the "reason" for step 5 of the proof?

Accepted Answer

CPCTC Theorem

Answer

Angle Bisector Theorem

Answer

Reflexive property

Answer

Proof

Question 6

How can you prove step #5?

Accepted Answer

Transitive property of congruence

Answer

Vertical angle theorem

Answer

Subtraction property of equality

Answer

Definition of supplementary angles

Question 7

How can you prove step #4?

Accepted Answer

Vertical angle theorem

Answer

Subtraction property of equality

Answer

Transitive property of congruence

Answer

Definition of supplementary angles

Question 8

Identify the missing statement or reason

Accepted Answer

Definition of Angle Bisector

Answer

Given

Answer

Vertical Angles Theorem

Answer

Alternate Interior Angles Theorem

Question 9

What reason justifies statement #2?

Accepted Answer

Definition of Midpoint

Answer

Transitive Property

Answer

Addition Property

Answer

Segment Addition Postulate

Answer

Substitution Property

Question 10

Based on the construction above which of the following are always true, choose all that apply.

Accepted Answer

Option A is correct

Accepted Answer

AE=EB

Accepted Answer

CE=ED

Accepted Answer

AC=BC

Answer

AB=CD

Question 11

Find x and the length of each segment.

Accepted Answer

x=8 WY=27, WZ=27

Answer

x=4 WY=15 WZ=15

Answer

x=9 WY=20 WZ=20

Answer

x=5 WY=16 WZ=16

Question 12

Find AE

Accepted Answer

12.5

Answer

18

Answer

11.75

Answer

13

Question 13

If you found the midpoint of line segment AB, what should you do next to find the equation of the perpendicular bisector?

Accepted Answer

Use the midpoint and slope perpendicular to AB to write the equation

Answer

Use the midpoint and one of the points from AB to write the equation

Answer

Use the distance and midpoint to find the equation

Answer

Skip it and hope it's not a test question

Question 14

Identify the perpendicular bisector.

Accepted Answer

$$\overleftarrow{\ T}\overrightarrow{P\ }$$

Answer

$$\overline{RS}$$

Answer

$$\overline{TR}$$

Answer

$$\overline{ST}$$

Question 15

In a line segment AB = 5.6 cm and its perpendicular bisector. Measure the length of each part.

Accepted Answer

2.8 cm

Answer

2.7 cm

Answer

2.9 cm

Answer

2.6 cm

Question 16

A perpendicular bisector is a LINE that is perpendicular to a segment at its midpoint. If segment AB has endpoints A (2, 6) and B(-4, -10) find the equation of the perpendicular bisector of segment AB. (It must have a slope that is the opposite reciprocal of the slope of AB and contain the midpoint of AB)

Accepted Answer

y + 2 = (3/8)(x + 1

Answer

y + 2 = -(3/8)(x +1)

Answer

y + 2 = (3/8)(x - 1)

Answer

y - 2 = (3/8)(x - 1)

Question 17

Marsha is using a straightedge and compass to do the construction shown. Which best describes the construction Marsha is doing?

Accepted Answer

a line through P parallel to line l

Answer

a line through P intersecting line l

Answer

a line through P congruent to line l

Answer

a line through P perpendicular to line l

Proving and Using Geometric Properties

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