Quiz about Congruence

Question 1

Consider parallelogram $$A B C D$$ with point $$X$$ at the intersection of diagonal segments $$A C$$ and $$B D$$.

![](http://admin.getprephub.com/media/editor/Screenshot%202023-05-16%20at%2012.39.30%20PM_20230516103944120784.png)
Evelyn claims that $$A B C D$$ is a square. Select the statement that must be true for Evelyn's claim to be true.

Accepted Answer

Covalent bond

Answer

$$A D=A B$$

Answer

$$A B=B D$$

Answer

$$A C=B X$$

Answer

$$m \angle A B C 
eq 90^{\circ}$$

Question 2

Leslie was able to map $$\overline{S T}$$ onto $$\overline{Q R}$$ using a rotation and dilation.

![](http://admin.getprephub.com/media/editor/con1_20230131180552648083.png)

Leslie concluded:

"I was able to map $$\overline{S T}$$ onto $$\overline{Q R}$$ using a sequence of rigid transformations, so the figures are congruent.

What error did Leslie make in her conclusion?

Accepted Answer

Covalent bond

Answer

Leslie didn't use only rigid transformations, so the figures are not congruent.

Answer

It's possible to map $$\overline{S T}$$ onto $$\overline{Q R}$$ using a sequence of rigid transformations, but the figures are not congruent.

Answer

There is no error. This is a correct conclusion.

Answer

None of the above.

Question 3

In quadrilateral $$A B C D, \overline{A B} \cong \overline{C D}$$ and $$\overline{B C} \cong \overline{A D}$$, as shown.

![](http://admin.getprephub.com/media/editor/Screenshot%202023-08-08%20at%206.23.02%20PM_20230808162324202514.png)

Select the correct statement to complete the proof showing that $$	riangle A B C \cong 	riangle C D A$$

Accepted Answer

Covalent bond

Answer

$$\overline{A C} \cong \overline{C A}$$

Answer

$$\overline{A B} \cong \overline{A D}$$

Answer

$$ \angle A B C \cong \angle C D A$$

Answer

$$\angle B A C \cong \angle A C D$$

Question 4

Triangle $$PQR$$ is shown, where $$S T$$ is parallel to $$R Q$$.

![](http://admin.getprephub.com/media/editor/gp21_20230225211656883271.png)

Marta wants to prove that $$\frac{S R}{P S}$$.

Choose the correct option or reason in the blank box to complete Marta's proof.

![](http://admin.getprephub.com/media/editor/gp21s_20230225211708372526.png)

Accepted Answer

Covalent bond

Answer

Corresponding sides of similar triangles are proportional.

Answer

{ASA similarity}

Answer

SSS similarity

Answer

Corresponding sides of similar triangles are congruent.

Question 5

Ioana tried to prove that $$	riangle O P Q \cong 	riangle S R Q$$

![](http://admin.getprephub.com/media/editor/con14_20230131185101928721.png)

Accepted Answer

Covalent bond

Answer

Ioana established all necessary conditions, but then used an inappropriate congruence criterion.

Answer

Ioana used an invalid reason to justify the congruence of a pair of sides or angles.

Answer

Ioana only established some of the necessary conditions for a congruence criterion.

Answer

loana used a criterion that does not guarantee congruence.

Congruence High School Geometry Maths Problems and Solutions

Many students find Congruence for High School Geometry particularly challenging. Strengthen your concepts and gain confidence for your exams by solving free questions for Congruence from for High School Geometry preparation.