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03-07-2022
Mathematics

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akposevictor akposevictor · Answer 1 · 2022-07-14T14:46:07-04:00

The statements and reasons that complete the proof are:

4. ∠SPQ ≅ ∠TQR [alternate interior angles theorem]

5. ΔPQS ≅ ΔQRT [ASA congruence theorem]

What is the ASA Congruence Theorem?

When two pairs of corresponding angles and one pair of included sides of two triangles are congruent, they are congruent triangles based on the ASA congruence theorem.

We are given the following:

QT ≅ PS [a pair of congruent sides]

∠T ≅ ∠S [a pair of congruent angles]

Thus, since QT is parallel to PS, therefore:

∠SPQ ≅ ∠TQR [alternate interior angles theorem]

Therefore, we can now state that ΔPQS ≅ ΔQRT based on the ASA congruence theorem.

Learn more about the ASA congruence theorem on:

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Sagot :

What is the ASA Congruence Theorem?

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