Question

In triangles ABC and PQR, given side lengths are in centimeters. Which rule or theorem can be applied to prove the similarity or congruence of these triangles?

a. Pythagorean theorem
b. Sine rule
c. Cosine rule
d. Angle-angle criterion

Answer 1

To demonstrate similarity or congruence between triangles ABC and PQR, the Pythagorean theorem is not applicable as it pertains only to right triangles. The Angle-Angle criterion should be used for similarity, while congruence can be determined with SSS, SAS, or ASA criteria. Therefore correct option is D

Step-by-step explanation:

To prove the similarity or congruence of triangles ABC and PQR using given side lengths, we cannot use the Pythagorean theorem as it only applies to right triangles. However, the correct approach would be to use the Angle-Angle (AA) criterion. This criterion states that if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

Similarity of triangles is based on the proportionality of their respective sides and the equality of their corresponding angles. Congruence requires exact match in shape and size, which can be determined using Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA) criteria.