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In triangle PQR, if PQ = 12 cm, PR = 9 cm, and QR = 15 cm, which criterion can b

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Question: In triangle PQR, if PQ = 12 cm, PR = 9 cm, and QR = 15 cm, which criterion can be used to prove that triangle PQR is not congruent to triangle STU with sides ST = 12 cm, SU = 9 cm, and TU = 14 cm?

Options:

  1. SSS
  2. SAS
  3. ASA
  4. AAS

Correct Answer: SSS

Solution: 

Triangle PQR cannot be congruent to triangle STU by SSS since the third side QR (15 cm) is not equal to TU (14 cm).

In triangle PQR, if PQ = 12 cm, PR = 9 cm, and QR = 15 cm, which criterion can b

Practice Questions

Q1
In triangle PQR, if PQ = 12 cm, PR = 9 cm, and QR = 15 cm, which criterion can be used to prove that triangle PQR is not congruent to triangle STU with sides ST = 12 cm, SU = 9 cm, and TU = 14 cm?
  1. SSS
  2. SAS
  3. ASA
  4. AAS

Questions & Step-by-Step Solutions

In triangle PQR, if PQ = 12 cm, PR = 9 cm, and QR = 15 cm, which criterion can be used to prove that triangle PQR is not congruent to triangle STU with sides ST = 12 cm, SU = 9 cm, and TU = 14 cm?
  • Step 1: Identify the sides of triangle PQR. They are PQ = 12 cm, PR = 9 cm, and QR = 15 cm.
  • Step 2: Identify the sides of triangle STU. They are ST = 12 cm, SU = 9 cm, and TU = 14 cm.
  • Step 3: Compare the lengths of the sides of both triangles. The sides of triangle PQR are 12 cm, 9 cm, and 15 cm. The sides of triangle STU are 12 cm, 9 cm, and 14 cm.
  • Step 4: Check if all three sides of triangle PQR are equal to the corresponding sides of triangle STU. The first two sides (PQ and ST, PR and SU) are equal, but the third sides (QR and TU) are not equal (15 cm vs 14 cm).
  • Step 5: Since the third sides are not equal, triangle PQR cannot be congruent to triangle STU by the SSS (Side-Side-Side) criterion.
  • Triangle Congruence Criteria – Understanding the Side-Side-Side (SSS) criterion for triangle congruence, which states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
  • Comparison of Side Lengths – Analyzing and comparing the lengths of the sides of two triangles to determine congruence.
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