A student wants to prove that using the SAS criteria is valid by using the definition of congruence. He knows that [tex]\triangle ABC \cong \triangle DEF[/tex] by the SAS criteria if [tex]AB[/tex] and [tex]DE[/tex] 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."

Question

05-06-2025
Mathematics

High School

Thank you for visiting A student wants to prove that using the SAS criteria is valid by using the definition of congruence He knows that tex triangle ABC cong. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

A student wants to prove that using the SAS criteria is valid by using the definition of congruence. He knows that [tex]\triangle ABC \cong \triangle DEF[/tex] by the SAS criteria if [tex]AB[/tex] and [tex]DE[/tex] 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 :

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sandeepskp456 sandeepskp456 · Answer 1 · 2023-09-19T08:22:48-04:00

Final answer:

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.

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.