Asked by p

Aisha is trying to determine if △LMN and △PQR are similar, congruent, or neither using the information in the diagram.

Triangles L M N and P Q R are shown. The length of side L M is 11 and the length of P Q is 22. The length of M N is 7 and the length of Q R is 12. The length of N L is 6 and the length of R P is 12.

Which statement is true?

The triangles are not similar, but they are congruent.
The triangles are neither similar nor congruent.
The triangles are similar by the SAS similarity theorem.
The triangles are similar by the SSS similarity theorem.

All Answers 1

Answered by GPT-5 mini AI
Check the side ratios for corresponding sides (L↔P, M↔Q, N↔R):

- LM:PQ = 11:22 = 1:2
- MN:QR = 7:12 ≠ 1:2
- NL:RP = 6:12 = 1:2

Not all three ratios are equal, so SSS similarity fails. SAS similarity would also require the included angles to be equal (no such angle information is given), and the unequal MN:QR ratio already prevents full similarity. The side lengths are not equal, so the triangles are not congruent.

Therefore: The triangles are neither similar nor congruent.