Geometry Help

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Practice for Test 1 Joseph Sigmon

Question 1 1/1 pt 99

Question 2 0/1 pt 5 99

Question 3 0/1 pt 5 99

Choose the correct words to fill in the blanks below.

line segment midpoint complementary congruent vertical supplementary vertex endpoint ray

1. A ray is a line segment that extends indefinitely

in one direction, and starts with a point or endpoint .

2. The midpoint of a line segment is the point that divides the segment into

two segments of equal length.

3. The common end point of two rays that form an angle is called the vertex

.

4. Two angles that add to are called complementary angles, whereas, two angles

that add to are called supplementary angles.

5. When two angles are vertical , then they are congruent

and have equal measure.

90 ∘

180 ∘

The figure shows between and .

a. Find :       b. Find :

c. Find :     d. Find :

e. What is the coordinate of ?

M A B

− 17 34

5x − 3 6x − 1

x ¯̄¯̄¯̄¯AM

¯̄¯̄¯̄¯M B ¯̄¯̄¯̄AB

M

The figure shows between and . M A B

x 2

x 7x + 9

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Question 4 0/1 pt 5 99

Question 5 0/1 pt 5 99

a. Find :       b. Find :

c. Find :     d. Find :

e. What is the coordinate of ?

− 12 37

x − x 7x + 9

x ¯̄¯̄¯̄¯AM

¯̄¯̄¯̄¯M B ¯̄¯̄¯̄AB

M

is the midpoint of the line

a.     b.

c.     d.

B ¯̄¯̄¯̄AC .

5(x − 2) x + 6

x = ¯̄¯̄¯̄AB =

¯̄¯̄¯̄BC = ¯̄¯̄¯̄AC =

bisects . ¯̄¯̄¯̄BC ∠ABD

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Question 6 0/1 pt 5 99

Question 7 0/1 pt 5 99

Note: Figure not necessarily drawn to scale.

a.

b. degrees

c. degrees

d. degrees

(4x + 5) ∘

(7x + 2) ∘

x =

∠ABC =

∠CBD =

∠ABD =

bisects .

Note: Figure not necessarily drawn to scale.

a.

b. degrees

c. degrees

d. degrees

¯̄¯̄¯̄BC ∠ABD

(6x + 7) ∘

(7x − 4) ∘

x =

∠ABC =

∠CBD =

∠ABD =

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Question 8 1/1 pt 99

Question 9 1/1 pt 99

Solve for the angles below.

Note: Figure not drawn to scale.

a. Find .

b. Find . degrees

c. Find . degrees

d. Find . degrees

(6x + 6) ∘

126 ∘

x

m∠1

m∠3

m∠4

Choose the correct words to fill in the blanks below.

contrapositive conditional inverse converse

1. A conditional statement has two parts, a hypothesis and a conclusion.

2. The converse of a conditional statement is formed by switching the

hypothesis and conclusion.

3. The inverse of a conditional statement is formed by negating the

hypothesis and conclusion.

4. The contrapositive of a conditional statement is formed by switching and negating

the hypothesis and conclusion.

For the conditional statement below, give the converse, the inverse, and the contrapositive.

If it is a square, then it is a rectangle.

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Question 10 1/1 pt 99

Question 11 1/1 pt 99

Question 12 1/1 pt 99

 Converse

 Inverse

 Contrapositive

a. If it is a rectangle, then it is a square.

b. If it is not a rectangle, then it is not a square.

c. If it is not a square, then it is not a rectangle.

t s a squa e, t e t s a ecta gle.

 

a

c

b

 Converse

 Inverse

 Contrapositive

a. If good is not enough, then better is possible.

b. If better is not possible, then good is enough.

c. If good is enough, then better is not possible.

For the conditional statement below, give the converse, the inverse, and the contrapositive.

If better is possible, then good is not enough.

 

a

b

c

Select the counterexample to the biconditional statement.

It is day time if and only if the sun is out.

It's night time.

It's night time and it's cloudy.

It's day time and it's cloudy.

Rewrite the biconditional statement as a conditional statement and then as its converse.

The rectangle is a square if and only if all 4 sides of the rectangle have the same length.

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Question 13 1/1 pt 99

Question 14 0/1 pt 5 99

e ecta gle s a squa e a d o ly all s des o t e ecta gle ave t e sa e le gt .

Conditional statement: If , then

.

Converse: If , then

.

the rectangle is a square

all 4 sides of the rectangle of the same length

all 4 sides of the rectangle of the same length

the rectangle is a square

For the problem, find the measure of the angle using the given information and the figure below.

26

m∠4 = 154 ∘

m∠7 =

Use the theorems of parallel lines to solve for in the following. x

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Question 15 1/1 pt 99

Question 16 0/1 pt 5 99

(14x + 14) ∘

(8x − 10) ∘

x =

Prove the Alternate Interior Angle Converse.

Steps Reasons Given

1 2 3 4

5 6

7 8

1. ∠3 ≅ ∠6

2. ∠3 ≅ ∠2 Vertical Angles Theorem

3. ∠6 ≅ ∠2 Transitive Property of Congruence

4. l1 ∥ l2 Corresponding Angles Postulate

Determine the measure of each indicated angle. Note: the figure is not drawn to scale.

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Question 17 0/1 pt 5 99

Question 18 0/1 pt 5 99

Note: Always make sure the value of produces positive angles.

: °

: °

: °

158 ∘

(6x + 9) ∘

(5x − 5) ∘

x

x =

m∠CAB

m∠ACB

m∠ABC

Determine the measure of each indicated angle. Note: the figure is not drawn to scale.

°

°

°

°

99 ∘

138 ∘∠1

m∠ACB =

m∠CBA =

m∠BAC =

m∠1 =

Determine the measure of each indicated angle. Note: the figure is not drawn to scale.

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Question 19 1/1 pt 99

Question 20 1/1 pt 99

Note: Always make sure the value of produces positive angles.

°

°

°

(6x + 2) ∘

(8x + 9) ∘

(10x + 13) ∘

x

x =

m∠ACB =

m∠CBA =

m∠BAC =

Which of the following must be true if two triangles are congruent?

Corresponding sides and angles are congruent.

Corresponding angles are congruent.

Corresponding sides or angles are congruent.

Corresponding sides are congruent.

Complete the congruence statement: ΔHIJ ≅

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Question 21 0/1 pt 5 99

Question 22 1/1 pt 99

ΔM KL

ΔKLM

ΔLKM

ΔKM L

is congruent to . Find and then and .

Note: Always make sure the value of produces positive lengths.

ΔABC ΔDEF x ¯̄¯̄¯̄AB ¯̄¯̄¯̄DE

A

B

C

14 − 6x D

E

F 8 − 8x

x

x =

¯̄¯̄¯̄AB =

¯̄¯̄¯̄DE =

Which of the following is NOT a congruence postulate?

Side-Angle-Side Postulate

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Question 23 1/1 pt 99

Question 24 0.5/1 pt 1 99

g

Angle-Angle-Angle Postulate

Side-Side-Side Postulate

Angle-Side-Angle Postulate

Which of the following is NOT a congruence postulate?

Angle-Angle-Side Postulate

Side-Side-Angle Postulate

Side-Angle-Side Postulate

Angle-Side-Angle Postulate

Side-Angle-Side (SAS)

Determine which postulate can be used to prove the triangles are congruent.

b

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Question 25 1/1 pt 99

 Side Angle Side (SAS)

 No Solution

 Angle-Side-Angle (ASA)

 Side-Side-Side (SSS)

a.

b.

c.

d.

 

b

c

d

a

Determine which postulate can be used to prove the triangles are congruent.

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Question 26 1/1 pt 99

Question 27 1/1 pt 99

Not enough information

ASA

AAS

SSS

SAS

Determine which postulate can be used to prove the triangles are congruent.

Not enough information

AAS

SAS

SSS

ASA

Select the correct reason for each step in the proof.

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Question 28 1/1 pt 99

Question 29 0/1 pt 5 99

Steps Reasons

Given1. ¯̄¯̄¯̄AB ≅¯̄¯̄¯̄DE

2. ∠ACB ≅ ∠DCE Vertical Angles Theorem

3. ∠BAC ≅ ∠DEC Alternate Interior Angle Theorem

4. ΔABC ≅ ΔEDC AAS

Select the correct reason for each step in the proof.

Let be the midpoint of and .

Steps Reasons

C ¯̄¯̄¯̄AE ¯̄¯̄¯̄BD

1. ∠ACB ≅ ∠DCE Vertical Angles Theorem

2. ¯̄¯̄¯̄AC ≅¯̄¯̄¯̄CE Definition of midpoints

3. ¯̄¯̄¯̄BC ≅¯̄¯̄¯̄CD Definition of midpoints

4. ΔABC ≅ ΔEDC SAS

Find and then and . x ¯̄¯̄¯̄AB ¯̄¯̄¯̄BC

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Question 30 0/1 pt 5 99

Question 31 0/1 pt 5 99

Note: Always make sure the value of produces positive lengths.

5x − 6 4x − 1

x

x =

¯̄¯̄¯̄AB =

¯̄¯̄¯̄BC =

Find the measure of . ∠BAC

36 ∘

m∠BAC =

Find and then and . x m∠BAC m∠BCA

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Note: Always make sure the value of produces positive angles.

°

°

(6x − 7) ∘

62 ∘

x

x =

m∠BAC =

m∠BCA =