Question

A student wants to prove that using the SAS criteria is valid by using the definition of congruence. He knows that AABC ~ADEF by the SAS criteria if AB and DE are shown to be one pair of congruent sides. Which statement uses the definition of congruence to support his conjecture?

A) "If two triangles have two pairs of corresponding angles that are congruent and one pair of corresponding sides that are congruent, then the triangles are congruent by the SAS criteria."

B) "If two triangles have one pair of corresponding sides that are congruent and the included angles are congruent, then the triangles are congruent by the SAS criteria."

C) "If two triangles have one pair of corresponding angles that are congruent and the included sides are congruent, then the triangles are congruent by the SAS criteria."

D) "If two triangles have two pairs of corresponding sides that are congruent and the included angle is congruent, then the triangles are congruent by the SAS criteria."

Answer 1

The best option to support the conjecture that triangles are congruent by SAS criteria is option B, which correctly states the need for one pair of congruent sides and the included angles to be congruent.

Step-by-step explanation:

The concept you're asking about belongs to the field of geometry, specifically discussing triangle congruence criteria. To prove two triangles are congruent using the SAS (Side-Angle-Side) criterion, you need one pair of congruent sides and the included angle to be congruent. Option B states, "If two triangles have one pair of corresponding sides that are congruent and the included angles are congruent, then the triangles are congruent by the SAS criteria." This option directly reflects the definition of congruence using SAS, where the included angle means the angle formed by the two sides you are comparing.