Quiz about Intro to Proofs Review

Question 1

B is the midpoint of AC.

Choose the correct statement based on the given information.

Accepted Answer

$$\overline{AB}\cong\overline{BC}$$

Answer

$$AB+BC=AC$$

Answer

$$\overline{AB}\cong\overline{AC}$$

Answer

$$\angle A\cong\angle C$$

Question 2

$$\overline{EG}$$ bisects $$\angle DEF.$$

Choose the correct statement based on the given information.

Accepted Answer

$$\angle DEG\cong\angle FEG$$

Answer

$$\overline{ED}\cong\overline{EF}$$

Answer

$$\angle D\cong\angle F$$

Answer

$$\angle DEG\cong\angle DEF$$

Question 3

$$\angle HIL$$ and $$\angle KIJ$$ are vertical angles.

Choose the correct statement based on the given information.

Accepted Answer

$$\angle HIL\cong\angle KIJ$$

Answer

$$\overline{HI}\cong\overline{IK}$$

Answer

$$\angle HIL\cong\angle LIK$$

Answer

I is the midpoint of $$\overline{LJ}$$

Question 4

$$\Delta MNO$$ is an isosceles triangle.

Choose the correct statement based on the given information.

Accepted Answer

$$\overline{NO}\cong\overline{MO}$$

Answer

$$\angle M\cong\angle O$$

Answer

$$\overline{NM}\cong\overline{MO}$$

Answer

$$\Delta MNO$$ is an equilateral triangle

Question 5

$$\Delta PQR$$ is an equilateral triangle.

SELECT ALL correct statements based on the given information.

Accepted Answer

$$\overline{PQ}\cong\overline{QR}$$

Accepted Answer

$$\overline{PQ}\cong\overline{PR}$$

Answer

$$PQ+QR=PR$$

Answer

$$\angle P+\angle R=90\degree$$

Question 6

$$\overline{VT}\perp\overline{US}$$

Choose the correct statement based on the given information.

Accepted Answer

$$\angle UTV$$ and $$\angle STV$$ are right angles

Answer

$$\overline{UT}\cong\overline{TS}$$

Answer

T is the midpoint of $$\overline{US}$$

Answer

$$\overline{VT}\cong\overline{US}$$

Question 7

$$\overline{WX}\parallel\overline{YZ}$$

Choose the correct statement based on the given information.

Accepted Answer

$$\angle X\cong\angle Y$$

Answer

$$\overline{WX}\cong\overline{YZ}$$

Answer

$$\angle X+\angle Y=90\degree$$

Answer

$$\overline{WX}\cong\overline{YX}$$

Question 8

$$\overline{BD}$$ bisects $$\angle ADC.$$

Choose the correct statement based on the given information.

Accepted Answer

$$\angle ADB\cong\angle CDB$$

Answer

$$\overline{AD}\cong\overline{DC}$$

Answer

$$\angle ABD$$ and $$\angle CBD$$ are right angles

Answer

$$\overline{AB}\cong\overline{BC}$$

Question 9

B is the midpoint of $$\overline{AC}$$

Choose the correct statement based on the given information.

Accepted Answer

$$\overline{AB}\cong\overline{BC}$$

Answer

$$\overline{AD}\cong\overline{DC}$$

Answer

$$\angle ABD$$ and $$\angle CBD$$ are right angles

Answer

$$\angle ADB\cong\angle CDB$$

Question 10

$$\Delta ADC$$ is an equilateral triangle.

Choose the correct statement based on the given information.

Accepted Answer

$$\overline{AD}\cong\overline{DC}$$

Answer

$$\angle ABD$$ and $$\angle CBD$$ are right angles

Answer

$$\angle ADB\cong\angle CDB$$

Answer

$$\overline{AB}\cong\overline{BC}$$

Question 11

$$\overline{DB}\perp\overline{AC}$$

Choose the correct statement based on the given information.

Accepted Answer

$$\angle ABD$$ and $$\angle CBD$$ are right angles

Answer

$$\overline{AD}\cong\overline{DC}$$

Answer

$$\angle ADB\cong\angle CDB$$

Answer

$$\overline{AB}\cong\overline{BC}$$

Question 12

$$\overline{EF}\parallel\overline{IH}$$

Choose the correct statement based on the given information.

Accepted Answer

$$\angle F\cong\angle I$$

Answer

$$\overline{EF}\cong\overline{IH}$$

Answer

$$\angle EGF\cong\angle HGI$$

Answer

$$\overline{EG}\cong\overline{HG}$$

Question 13

$$\angle EGF$$ and $$\angle HGI$$ are vertical angles.

Choose the correct statement based on the given information.

Accepted Answer

$$\angle EGF\cong\angle HGI$$

Answer

$$\overline{EF}\cong\overline{IH}$$

Answer

$$\angle F\cong\angle I$$

Answer

$$\overline{EG}\cong\overline{HG}$$

Question 14

G is the midpoint of $$\overline{EH}$$

Choose the correct statement based on the given information.

Accepted Answer

$$\overline{EG}\cong\overline{HG}$$

Answer

$$\overline{EF}\cong\overline{IH}$$

Answer

$$\angle F\cong\angle I$$

Answer

$$\angle EGF\cong\angle HGI$$

Question 15

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

SSS

Answer

SAS

Answer

ASA

Answer

AAS

Answer

Cannot be proved congruent

Question 16

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

ASA

Answer

SSS

Answer

SAS

Answer

AAS

Answer

Cannot be proved congruent

Question 17

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

Cannot be proved congruent

Answer

SSS

Answer

SAS

Answer

ASA

Answer

AAS

Question 18

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

Cannot be proved congruent

Answer

SSS

Answer

SAS

Answer

ASA

Answer

AAS

Question 19

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

SSS

Answer

SAS

Answer

ASA

Answer

AAS

Answer

Cannot be proved congruent

Question 20

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

SAS

Answer

SSS

Answer

ASA

Answer

AAS

Answer

Cannot be proved congruent

Question 21

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

AAS

Answer

SSS

Answer

SAS

Answer

ASA

Answer

Cannot be proved congruent

Question 22

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

Cannot be proved congruent

Answer

SSS

Answer

SAS

Answer

ASA

Answer

AAS

Question 23

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

SAS

Answer

SSS

Answer

ASA

Answer

AAS

Answer

Cannot be proved congruent

Question 24

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

Cannot be proved congruent

Answer

SSS

Answer

SAS

Answer

ASA

Answer

AAS

Question 25

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

Cannot be proved congruent

Answer

SSS

Answer

SAS

Answer

ASA

Answer

AAS

Question 26

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

ASA

Answer

SSS

Answer

SAS

Answer

AAS

Answer

Cannot be proved congruent

Question 27

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

Cannot be proved congruent

Answer

SSS

Answer

SAS

Answer

ASA

Answer

AAS

Question 28

Which triangle congruence theorem can be used to show the triangles are congruent?

Accepted Answer

AAS

Answer

SSS

Answer

SAS

Answer

ASA

Answer

Cannot be proved congruent

Question 29

What is Reason C?

Accepted Answer

Vertical Angle Theorem

Answer

Definition of Congruence

Answer

Definition of Vertical Angles

Answer

Reflexive Property

Question 30

Look at this partial proof, Notice the given information. What would be the reason for statment #2?

Accepted Answer

Definition of Midpoint

Answer

Definition of congruence

Answer

Transitive Property

Answer

Substitution Property

Question 31

What is #3 Reason?

Accepted Answer

Alternate Interior Angles

Answer

Alternate Exterior Angles

Answer

Vertical Angles

Answer

Angle Bisector

Question 32

What is #4 Reason

Accepted Answer

Segment Bisector

Answer

Definition of Midpoint

Answer

Perpendicular Bisector

Answer

Reflexive Property

Question 33

Given

$$\Delta ABC\ \cong\Delta DEF\ $$
$$\angle A\ \cong\ ?$$

Accepted Answer

$$\angle D$$

Answer

$$\angle E$$

Answer

$$\angle F$$

Answer

$$\angle C$$

Question 34

Given Hexagons

$$ABCDEF\ \cong PQRSTU$$
$$\overline{DC}\ \cong?$$

Accepted Answer

$$\overline{SR}$$

Answer

$$\overline{RS}$$

Answer

$$\overline{PQ}$$

Answer

$$\overline{ST}$$

Answer

$$\overline{UT}$$

Question 35

$$\Delta PET\cong\Delta DOG$$

Which of the following are TRUE

Accepted Answer

$$\angle P\cong\angle D$$

Accepted Answer

$$\overline{TE}\cong\overline{GO}$$

Accepted Answer

$$\overline{TP}\cong\overline{GD}$$

Answer

$$\angle T\cong\angle O$$

Answer

$$\overline{TE}\cong\overline{OG}$$

Question 36

Given

$$\Delta ABC\ \cong\Delta DEF\ $$
$$\overline{CA}\ \cong\ ?$$

Accepted Answer

$$\overline{FD}$$

Answer

$$\overline{DE}$$

Answer

$$\overline{EF}$$

Answer

$$\overline{DF}$$

Question 37

Given

$$\Delta ABC\ \cong\Delta DEF\ $$
$$\angle C\ \cong\ ?$$

Accepted Answer

$$\angle F$$

Answer

$$\angle D$$

Answer

$$\angle E$$

Answer

$$\angle A$$

Question 38

In the diagram below, $$\Delta PQR\cong\Delta XYZ$$ .

Based on the dimensions in the diagram, what is the length of $$\overline{YZ}?$$

Accepted Answer

4 in.

Answer

3 in.

Answer

5 in.

Answer

6 in.

Question 39

If Quadrilateral PQRS is congruent to Quadrilateral WXYZ, what is the measure of Angle W?

Accepted Answer

$$133\degree$$

Answer

$$45\degree$$

Answer

$$70\degree$$

Answer

$$112\degree$$

Question 40

A triangular tile is shown. Patrick needs another tile that is congruent to this tile for the design on his kitchen wall.

Which tile is congruent to the original tile?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 41

Which of the following is not a valid reason to prove congruent triangles?

Accepted Answer

SSA

Answer

ASA

Answer

SAS

Answer

SSS

Question 42

Which pair of triangles cannot be proven congruent?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Question 43

If $$\Delta ABC\cong\Delta XYZ$$ , select all of the congruence statements that are true.

Accepted Answer

$$\overline{CA}\cong\overline{ZX}$$

Accepted Answer

$$\angle C\cong\angle Z$$

Accepted Answer

$$\Delta ABC\sim\Delta XYZ$$

Answer

$$\angle A\cong\angle Y$$

Answer

$$\overline{AB}\cong\overline{YZ}$$

Question 44

Use $$\Delta BCD$$ and the fact that $$\Delta BCD\cong\Delta LMN$$ to determine the length of NM.

Accepted Answer

57

Answer

37

Answer

40

Answer

50

Question 45

Use $$\Delta BCD$$ and the fact that $$\Delta BCD\cong\Delta LMN$$ to determine the measure of $$\angle L.$$

Accepted Answer

80 degrees

Answer

60 degrees

Answer

40 degrees

Question 46

Identify the  missing statement or reason

Accepted Answer

Definition of Angle Bisector

Answer

Given

Answer

Vertical Angles Theorem

Answer

Alternate Interior Angles Theorem

Intro to Proofs Review

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