Question

Given line PQ bisects line RS, LR=LS
Prove: Triangle PQR= Triangle PQS

Answer 1

Answer:

See Below

Step-by-step explanation:

Since PQ is perpendicular to RS, the angles PQR and PQS would be right angles, and right anglers are congruent, so <PQR ≅ <PQS. We are given that <R and <S are the same length, so they are congruent(<R ≅ <S). Since PQ is included in both triangles and it is the same length as itself(PQ ≅ PQ).

We have three congruent parts, two angles and one side. Therefore, using AAS, ΔPQR ≅ ΔPQS

Answer 2

Answer:

See below ~

Step-by-step explanation:

Given :

⇒ PQ ⊥ RS

⇒ ∠R = ∠S

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Solving :

⇒ PQ = PQ (common side)

⇒ ∠R = ∠S (given)

⇒ ∠PQS = ∠PQR = 90° (⊥ bisector forms equal right angles)

⇒ ΔPQR ≅ ΔPQS (by ASA congruence)