8.3 Check Understanding and On Your Own

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.

• Yes, it is possible to draw two different triangles.

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

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

• Translation followed by rotation

• Reflection followed by translation

• Rotation followed by dilation

• Dilation followed by reflection

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

• The lengths of all three sides of both triangles

• The measure of all three angles of both triangles

• The area of both triangles

• The perimeter of both triangles

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?

• x = 4

• x = 5

• x = 6

• x = 7

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.

• Congruent by SSS

• Congruent by SAS

• Congruent by ASA

• Not congruent

• Not enough information

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.

• Congruent by SSS

• Congruent by SAS

• Congruent by ASA

• Not congruent

• Not enough information

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.

• Congruent by SSS

• Congruent by SAS

• Congruent by ASA

• Not Congruent

• Not enough information

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.

• The triangles are congruent by SSS theorem.

• The triangles are congruent by SAS theorem.

• The triangles are not congruent.

• There is not enough information to determine congruence.

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.

• Congruent by SSS

• Congruent by SAS

• Congruent by ASA

• Not congruent

• Not enough information

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.

• The triangles are congruent by SSS theorem.

• The triangles are congruent by SAS theorem.

• The triangles are not congruent.

• There is not enough information to determine congruence.