Try It

Congruent Triangles - SSS and SAS Practice

Practice Problem #1

Triangles FGH and KIJ. Angles H and I are marked congruent. Segments FH and IJ are marked congruent. Segments HG and KI are marked congruent.

Match the corresponding congruent parts of the triangles and reasons for congruence. Is this enough information to prove the triangles congruent? If so, complete the congruence statement and the method used to prove they are congruent.

  • segment FH ≅ ______
  • segment GH ≅ ______
  • ∠GHF ≅ ∠______
  • Yes, ΔFHG ≅ _____ by the _______ postulate.

Answer choices:

  • segment JIK
  • segment KI
  • SAS
  • JI
  • KIJ

Answers:

  • segment FH ≅ segment JI
  • segment GH ≅ segment KI
  • ∠GHF ≅ KIJ
  • Yes, ΔFHG ≅ JIK by the SAS postulate.

Practice Problem #2

Two triangles ABC and CDE intersecting at point C. Segments AB and ED are marked congruent. Segments AC and CE are marked congruent. Segments BC and CD are marked congruent.

Match the corresponding congruent parts of the triangles and reasons for congruence. Is this enough information to prove the triangles congruent? If so, complete the congruence statement and the method used to prove they are congruent.

  • segment AB ≅ ______
  • segment AC ≅ ______
  • segment BC ≅ ______
  • Yes, ΔABC ≅ Δ_____ by the _______ postulate.

Answer choices:

  • SSS
  • segment EC
  • segment ED
  • EDC
  • segment DC

Answers:

  • segment AB ≅ segment ED
  • segment AC ≅ segment EC
  • segment BC ≅ segment DC
  • Yes, ΔABC Δ≅ EDC by the SSS postulate.

Practice Problem #3

Is this enough information to prove the triangles congruent? If yes, list SSS or SAS as the method used to prove them congruent. Then identify the rigid transformation.

Is this enough information to prove the triangles congruent?
Answer: Yes

Method Used
Answer: SSS

Rigid Transformation:
Answer: Reflection

Practice Problem #4

Is this enough information to prove the triangles congruent? If yes, list SSS or SAS as the method used to prove them congruent. Then identify the rigid transformation.

Is this enough information to prove the triangles congruent?
Answer: No

Practice Problem #5

Is this enough information to prove the triangles congruent? If yes, list SSS or SAS as the method used to prove them congruent. Then identify the rigid transformation.

Is this enough information to prove the triangles congruent?
Answer: Yes

Method Used
Answer: SAS

Rigid Transformation:
Answer: Translation

Practice Problem #6

Verify that these triangles are congruent using the distance formula. You will need to prove that all three sides are congruent.

Segment BA is congruent to _____
Answer: segment MZ

The lengths of BA and ______ = ______
Answer: MZ = square root of 13

Segment BC is congruent to _____
Answer: segment MY

The lengths of BC and ______ = ______
Answer: MY = square root of 58

Segment CA is congruent to _____
Answer: segment YZ

The lengths of CA and ______ = ______
Answer: YZ = square root of 5

Complete the congruence statement. Δ ABC ≅ ______ by the ______ Postulate.
Answer: Δ ABC ≅ ΔZMY by the SSS Postulate.