Question

triangle pqr is an isosceles triangle and ps is altitude on the side of qr.Prove that triangle pqs is congurent to triangle prs

Answer 1

Ello there!

--------------------------

Question: ΔPQR is an isoceles triangle and PS is altitude on the side of QR. Prove that ΔPQS ≅ ΔPRS.

---------------------------

Pre-requisite Knowledge

You must be familiar with concepts related to Congruency, such as

• SSS congruency
• SAS congruency
• ASA conruency
• AAS congruency
• RHS congruency

---------------------------------

Answer

Given,

PQ = QR

PS is an altitude to the side QR

To Prove,

ΔPQS ≅ ΔPRS.

Proof,

In  ΔPQS and ΔPRS.

PQ = PR (given)

PS = PS (common side)

∠PSQ = ∠PSR = 90° (Altitude)

∴  ΔPQS ≅ ΔPRS by RHS congruency

(*Remember* RHS cannot be used when we simply obtain an angle is equal to 90°, We must get a Hypotenuse, Altitude and an 90° angle to use RHS congruency)

----------------------------

Hope It Helps!

Answer 2

Hey dear here is your answer!!!!!

___________________________

Let's note down the details we have been provided:-

PQR is an isosceles triangle.

Therefore, PQ = PR ( Equal sides of an isosceles triangle)

Now, in ΔPQS and ΔPRS:-

∠PSQ = ∠PSR (Altitude of an isosceles triangle form 90° with base)

PS = SP ( Common side)

PQ = PR ( Given )

Hence, ΔPQS ≅ ΔPRS. (RHS)

RHS congruency has been used because we had:-

• A pair of equal Hypotenuse
• A pair of equal angles 90° each
• A pair of equal sides

Therefore, ΔPQS is congruent to ΔPRS !

*NOTE* - I am providing an attachment for your better understanding !

❣️⭐ Hope it helps you dear...⭐⭐❣️❣️