Quiz about Triangle and Quadrilateral Proofs Quiz

Question 1

Which of the following is NOT one of the ways we prove 2 triangles to be congruent?

Accepted Answer

SSA

Answer

ASA

Answer

AAS

Answer

SAS

Question 2

If triangle D'E'F' is the image of triangle DEF, under which transformation will the triangles NOT be congruent?

Accepted Answer

dilation centered at the origin with a scale factor of 2

Answer

rotation of 180 degrees about the origin

Answer

reflection over the y-axis

Answer

translation 2 units left and 1 unit down

Question 3

Given: AN || CS. This would make angle NAK and angle CSK...

Accepted Answer

congruent alternate interior angles.

Answer

supplementary alternate interior angles.

Answer

congruent vertical angles.

Answer

supplementary vertical angles.

Question 4

Given: Triangle AKN and triangle CKS. This would make angle AKN and angle CKS...

Accepted Answer

congruent vertical angles.

Answer

congruent alternate interior angles.

Answer

supplementary alternate interior angles.

Answer

supplementary vertical angles.

Question 5

Given: AC and BD bisect each other at point E. Given this information, which of the following reasons could you use to prove triangle AEB congruent to triangle DEC?

Accepted Answer

SAS

Answer

SSS

Answer

ASA

Answer

AAS

Question 6

What is the best answer to give when describing why rigid motions (rotations, reflections, or translations) cause an image to be congruent to its preimage?

Accepted Answer

Rigid motions preserve distance and angle measure.

Answer

Rigid motions preserve size and shape.

Answer

Rigid motions preserve size and angle measure.

Answer

Rigid motions preserve distance and shape.

Question 7

Given - Angle A is congruent to angle X, Angle C is congruent to angle Z, and Side AC is congruent to side XZ. Based on this info, which reason would we use first to prove the two triangles congruent? Then, which reason would we use to prove angle B congruent to angle Y?

Accepted Answer

First ASA, then CPCTC

Answer

First AAS, then CPCTC

Answer

First CPCTC, then ASA

Answer

First CPCTC, then AAS

Question 8

Given: EA is perpendicular to side ZAT. A student then writes the statement "Angle EAT and angle EAZ are right angles." What is the reason for this?

Accepted Answer

perpendicular lines form right angles

Answer

all right angles are congruent

Answer

perpendicular angles are congruent

Answer

all right angles are perpendicular

Question 9

After you state that two angles are right, you may then state that the 2 angles are congruent. What will ALWAYS be the reason for this?

Accepted Answer

all right angles are congruent

Answer

perpendicular lines form right angles

Answer

hypotenuse leg

Answer

all right angles are perpendicular

Question 10

If it is given that X is the midpoint of RS, then you are ONLY allowing to make which of the following statement, and then reason?

Accepted Answer

RX is congruent to XS because a midpoint cuts a line segment in half.

Answer

TX is congruent to XV because a midpoint cuts a line segment in half.

Answer

TV is congruent to RS because a midpoint cuts a line segment in half.

Answer

TR is congruent to SV because a midpoint cuts a line segment in half.

Question 11

If it is given that EA is the angle bisector of angle ZET, then the ONLY statement and reason you are allowed to make at this point is...

Accepted Answer

angle ZEA is congruent to angle TEA because angle bisectors cut angles in half.

Answer

angle EAZ is congruent to angle EAT because angle bisectors cut angles in half.

Answer

angle ZEA is congruent to angle TEA because all right angles are congruent.

Answer

angle EAZ is congruent to angle EAT because all right angles are congruent.

Question 12

Without any given information, what are you allowed to state about the following diagram, and for what reason?

Accepted Answer

LN is congruent to LN by the reflexive property.

Answer

LN is congruent to LN by CPCTC.

Answer

LM is congruent to LO by the reflexive property.

Answer

MN is congruent to NO by CPCTC.

Question 13

The two triangles shown are overlapping. Which angle is congruent to itself by the reflexive property since both triangles share this angle?

Accepted Answer

Angle G

Answer

Angle H

Answer

Angle J

Answer

Angle K

Question 14

Given: AB and DC are both parallel and congruent. Why would angle ABD be congruent to angle CDB?

Accepted Answer

alternate interior angles are congruent.

Answer

vertical angles are congruent.

Answer

opposite angles of a parallelogram are congruent.

Answer

corresponding angles are congruent.

Question 15

Given: Side AB is congruent to side BC. Which type of triangle is this, and which 2 angles would then be congruent as a result of AB congruent to BC?

Accepted Answer

isosceles; angle A is congruent to angle C

Answer

equilateral; angle B is congruent to angle C

Answer

right triangle; angle A is congruent to angle C

Answer

isosceles; angle A is congruent to angle B

Question 16

Given - Parallelogram ABCD with both pairs of opposite sides congruent (AB is congruent to DC AND AD is congruent to BC). Which theorem would prove the two triangle congruent?

Accepted Answer

SSS

Answer

SAS

Answer

AAS

Answer

ASA

Question 17

Given - BED bisects AC. What is the ONLY statement and reason you are able to make at this point in the proof?

Accepted Answer

AE is congruent to EC because segment bisectors cut line segments in half.

Answer

BE is congruent to ED because segment bisectors cut line segments in half.

Answer

BD is congruent to AC because segment bisectors cut line segments in half.

Answer

angles AED and DEC are congruent vertical angles.

Question 18

Given - AE is congruent to EC and DE is congruent to EB in parallelogram ABCD. Which property does this demonstrate?

Accepted Answer

the diagonals of a parallelogram bisect each other.

Answer

opposite sides of a parallelogram are congruent.

Answer

the diagonals cut a parallelogram into 2 congruent triangles.

Answer

the diagonals of a parallelogram are perpendicular.

Question 19

Given: Parallelogram ABCD. Side DC is parallel to AB. Therefore, angle ADB is congruent to which other angle, and why?

Accepted Answer

DBC; 2 parallel lines cut by a transversal create congruent alternate interior angles.

Answer

BDC; 2 parallel lines cut by a transversal create congruent alternate interior angles.

Answer

DBC; opposite angles in a parallelogram are congruent.

Answer

BDC; opposite angles in a parallelogram are congruent.

Question 20

Both pairs of opposite sides of a parallelogram...

Accepted Answer

are congruent and parallel.

Answer

are parallel and perpendicular.

Answer

are congruent and perpendicular.

Answer

bisect each other.

Question 21

Which pairs of angles shown in parallelogram ABCD are opposite angles, and what is their relationship?

Accepted Answer

A and C, B and D; they are congruent

Answer

A and B, D and C; they are supplementary

Answer

A and B, D and C; they are congruent

Answer

A and C, B and D; they are supplementary

Question 22

Which pairs of angles shown in parallelogram ABCD are consecutive (adjacent) angles, and what is their relationship?

Accepted Answer

A and B, D and C; they are supplementary

Answer

A and C, B and D; they are congruent

Answer

A and B, D and C; they are congruent

Answer

A and C, B and D; they are supplementary

Question 23

A parallelogram must be a rhombus if its diagonals...

Accepted Answer

bisect the angles.

Answer

bisect each other.

Answer

intersect at a point.

Answer

are congruent.

Question 24

A parallelogram must be a rectangle if...

Accepted Answer

the diagonals are congruent.

Answer

the diagonals are perpendicular.

Answer

it has 2 adjacent congruent sides.

Answer

opposite sides are parallel.

Question 25

A parallelogram with 1 right angle is a...

Accepted Answer

rectangle

Answer

rhombus

Answer

square

Answer

all parallelograms

Question 26

A parallelogram with diagonals that are perpendicular and 2 congruent adjacent sides best describes

Accepted Answer

a rhombus

Answer

all parallelograms

Answer

a rectangle

Answer

a square

Question 27

A parallelogram with 1 right angle and 2 adjacent congruent sides has to be a...

Accepted Answer

square

Answer

rectangle

Answer

rhombus

Answer

this is true for all parallelograms.

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