Free Printable 8.3 Check Understanding and On Your Own

1.

Two triangles have side lengths of 3 inches, 4 inches, and 5 inches. Is it possible to draw two different triangles that meet this criteria? Justify your answer.

a)

Yes, it is possible to draw two different triangles.

b)

no; If two triangles have 3 congruent side lengths, the triangles must be congruent

2.

Describe a set of transformations that maps △ABC to △DEF.

a)

Translation followed by rotation

b)

Reflection followed by translation

c)

Rotation followed by dilation

d)

Dilation followed by reflection

3.

What additional information is needed to use the SSS Triangle Congruence Theorem to prove that the triangles are congruent?

a)

The lengths of all three sides of both triangles

b)

The measure of all three angles of both triangles

c)

The area of both triangles

d)

The perimeter of both triangles

4.

Triangles PQR and XYZ are equilateral triangles. The sides of △PQR are 5 inches long. One side of △XYZ is (2x – 3) inches. What value of x makes the triangles congruent?

a)

x = 4

b)

x = 5

c)

x = 6

d)

x = 7

5.

Determine whether the triangles are congruent, not congruent, or if there is not enough information. Which triangle congruence theorem can be used? Explain your reasoning. Triangle with sides marked in diagram.

a)

Congruent by SSS

b)

Congruent by SAS

c)

Congruent by ASA

d)

Not congruent

e)

Not enough information

6.

Determine whether the triangles are congruent, not congruent, or if there is not enough information. Which triangle congruence theorem can be used? Explain your reasoning. Triangle with sides marked in diagram.

a)

Congruent by SSS

b)

Congruent by SAS

c)

Congruent by ASA

d)

Not congruent

e)

Not enough information

7.

In Problems 7–12, determine whether the triangles are congruent, not congruent, or if there is not enough information. Which triangle congruence theorem can be used? Explain your reasoning. Triangle with sides marked in diagram.

a)

Congruent by SSS

b)

Congruent by SAS

c)

Congruent by ASA

d)

Not Congruent

e)

Not enough information

8.

Determine whether the triangles are congruent, not congruent, or if there is not enough information. Which triangle congruence theorem can be used? Explain your reasoning. Triangle with sides marked in diagram.

a)

The triangles are congruent by SSS theorem.

b)

The triangles are congruent by SAS theorem.

c)

The triangles are not congruent.

d)

There is not enough information to determine congruence.

9.

Determine whether the triangles are congruent, not congruent, or if there is not enough information. Which triangle congruence theorem can be used? Explain your reasoning. Triangle with sides marked in diagram.

a)

Congruent by SSS

b)

Congruent by SAS

c)

Congruent by ASA

d)

Not congruent

e)

Not enough information

10.

Determine whether the triangles are congruent, not congruent, or if there is not enough information. Which triangle congruence theorem can be used? Explain your reasoning. Triangle with sides marked in diagram.

a)

The triangles are congruent by SSS theorem.

b)

The triangles are congruent by SAS theorem.

c)

The triangles are not congruent.

d)

There is not enough information to determine congruence.

11.

Identify a series of rigid transformations that maps $\triangle ABC$ onto $\triangle DEF$ .

a)

Translation followed by rotation

b)

Reflection followed by translation

c)

Rotation followed by reflection

d)

Translation followed by reflection

12.

Identify a series of rigid transformations that maps $\triangle ABC$ onto $\triangle DEF$ .

a)

Translation followed by rotation

b)

Reflection followed by translation

c)

Rotation followed by reflection

d)

Translation followed by reflection

13.

Find the values of $x$ and $y$ for which $\triangle ABC$ and $\triangle XYZ$ are congruent. $\triangle ABC$ : side lengths of 5, 8, and $x$ . $\triangle XYZ$ : side lengths of 5, 2x, and 4.

(a)

14.

Find the values of $x$ and $y$ for which $\triangle ABC$ and $\triangle XYZ$ are congruent. $\triangle ABC$ : side lengths of 10, 10, and $2x - 1$ . $\triangle XYZ$ : side lengths of 10, 10, and $4x - 4$ .

(a)

8.3 Check Understanding and On Your Own

Total questions: 14

Worksheet time: 8mins

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