Quiz about Triangles Congruence Mastery Quiz

Question 1

Which of the following is a criterion for triangle congruence?

Accepted Answer

Angle-Side-Angle (ASA)

Answer

Side-Side-Angle (SSA)

Answer

Angle-Angle-Side (AAS)

Answer

Side-Angle-Side (SAS)

Question 2

In triangle ABC and DEF, if AB = DE, $$\angle B = \angle E$$ , and BC = EF, which congruence theorem can be used to prove the triangles are congruent?

Accepted Answer

SAS

Answer

ASA

Answer

AAS

Answer

SSA

Question 3

If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, which theorem proves the triangles are congruent?

Accepted Answer

AAS

Answer

ASA

Answer

SAS

Answer

SSA

Question 4

What does CPCTC stand for?

Accepted Answer

Corresponding Parts of Congruent Triangles are Congruent

Answer

Congruent Points Congruent Triangles Correspondingly

Answer

Congruent Polygons Corresponding Triangles Congruently

Answer

Congruent Parts of Corresponding Triangles are Congruent

Question 5

Which of the following is NOT a valid congruence theorem for triangles?

Accepted Answer

SSA

Answer

SAS

Answer

ASA

Answer

AAS

Question 6

Given triangle ABC and triangle DEF, if $$\angle A = \angle D$$ , AC = DF, and $$\angle C = \angle F$$ , which congruence theorem can be used to prove the triangles are congruent?

Accepted Answer

AAS

Answer

ASA

Answer

SAS

Answer

SSA

Question 7

In proving triangles congruent, the Side-Side-Side (SSS) theorem states that:

Accepted Answer

If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

Answer

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Answer

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

Answer

If two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle, the triangles are congruent.

Question 8

Which theorem is applied when two triangles have two sides and the angle between them congruent?

Accepted Answer

SAS

Answer

ASA

Answer

AAS

Answer

SSS

Question 9

If $$ riangle ABC \cong riangle DEF$$ by the ASA Postulate, which of the following must be true?

Accepted Answer

$$\angle A = \angle D$$ , AB = DE, $$\angle B = \angle E$$

Answer

AB = DE, BC = EF, CA = FD

Answer

$$\angle A = \angle D$$ , $$\angle B = \angle E$$ , $$\angle C = \angle F$$

Answer

$$\angle B = \angle E$$ , BC = EF, $$\angle C = \angle F$$

Question 10

The AAS Congruence Theorem requires two angles and the non-included side to be congruent. If $$\angle ABC = \angle XYZ$$ and $$\angle BCA = \angle YZX$$ , which side must also be congruent to prove $$ riangle ABC \cong riangle XYZ$$ using AAS?

Accepted Answer

BC = YZ

Answer

AB = XY

Answer

AC = XZ

Answer

None of the above

Question 11

Which statement is true about the SSA condition?

Accepted Answer

It is not a valid congruence theorem for triangles.

Answer

It is a valid method to prove triangle congruence.

Answer

It can sometimes prove triangle congruence but is not reliable.

Answer

It is always a valid method to prove right triangles congruent.

Question 12

If two triangles are congruent by the SAS theorem, which of the following is true?

Accepted Answer

Both their corresponding sides and angles are congruent.

Answer

Their corresponding angles are congruent.

Answer

Their corresponding sides are congruent.

Answer

Only their corresponding sides adjacent to the angle are congruent.

Question 13

For which of the following conditions is the ASA Congruence Theorem applicable?

Accepted Answer

Two angles and the side between them are congruent.

Answer

Two sides and the angle opposite one of the sides are congruent.

Answer

Two angles and the side opposite one of the angles are congruent.

Answer

Two sides and the angle between them are congruent.

Question 14

When proving triangles congruent using CPCTC, which step comes immediately before applying CPCTC?

Accepted Answer

Establishing the congruence of the triangles using one of the congruence theorems.

Answer

Proving the triangles have at least one congruent side.

Answer

Identifying corresponding parts of the triangles.

Answer

Measuring all angles and sides of the triangles.

Question 15

Which of the following is NOT a step in proving triangles congruent using the AAS Congruence Theorem?

Accepted Answer

Prove the included sides are congruent.

Answer

Prove two pairs of corresponding angles are congruent.

Answer

Prove a pair of corresponding non-included sides are congruent.

Answer

Identify the two triangles being compared.

Question 16

In the context of triangle congruence, what does the term "included side" refer to?

Accepted Answer

The side between two angles being used in the congruence proof.

Answer

The side opposite the largest angle.

Answer

The side that is not used in the congruence proof.

Answer

The longest side of the triangle.

Question 17

If $$ riangle ABC \cong riangle DEF$$ by the SAS criterion, which of the following must be true?

Accepted Answer

AB = DE and BC = EF

Answer

$$\angle A = \angle D$$ and $$\angle B = \angle E$$

Answer

$$\angle B = \angle E$$ and BC = EF

Answer

AC = DF and $$\angle C = \angle F$$

Question 18

Which theorem or postulate states that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent?

Accepted Answer

AAS

Answer

SAS

Answer

SSS

Answer

ASA

Question 19

The Side-Angle-Side (SAS) Congruence Theorem is used when you know:

Accepted Answer

Two sides and the angle between them are congruent.

Answer

Two sides and an angle are congruent, and the angle is not between the two sides.

Answer

Two angles and a side are congruent, and the side is not between the two angles.

Answer

Two angles and the side between them are congruent.

Question 20

What is the primary reason the Side-Side-Angle (SSA) condition is not a valid congruence criterion?

Accepted Answer

It can lead to ambiguous cases where two different triangles can be formed.

Answer

It only applies to right triangles.

Answer

It is always a valid criterion but is less commonly used.

Answer

It does not take into account the angles of the triangles.

Question 21

When using CPCTC to prove corresponding parts of congruent triangles are congruent, which of the following is a necessary first step?

Accepted Answer

Proving that the triangles are congruent using a congruence theorem.

Answer

Proving that all sides of the triangles are congruent.

Answer

Identifying the corresponding parts of the triangles.

Answer

Measuring the angles of the triangles.

Question 22

Which of the following scenarios would NOT allow you to use the ASA Congruence Theorem to prove two triangles are congruent?

Accepted Answer

Two angles are congruent, and the side is not between them.

Answer

Two angles and the side opposite one of the angles are congruent.

Answer

Two angles and the side adjacent to one of the angles are congruent.

Answer

Two angles and the side between them are congruent.

Question 23

In triangle congruence, the term "corresponding parts" refers to:

Accepted Answer

Both A and B.

Answer

Parts that have the same measurements in both triangles.

Answer

Parts that are in the same position in both triangles.

Answer

Neither A nor B.

Question 24

Which of the following is a true statement about the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) congruence theorems?

Accepted Answer

ASA requires knowing two angles and the included side, while AAS requires two angles and any side.

Answer

Both can prove congruence without knowing any side lengths.

Answer

Both require knowing at least two side lengths.

Answer

AAS is a special case of ASA.

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