Question

QL, MR and PN, the three altitudes of the △PQR, are equal. △PQR is a/an _______ triangle.

• A. Isosceles
• B. Scalene
• C. Equilateral
• D. Right angled

Answer 1

The correct option is C

Equilateral

In $△QRL\text{and}△QRM$
$\angle QMR=\angle QLR={90}^o$ (Altitude)
QL = RM (Given)
QR is the common side

$\Rightarrow$ △QRL ≅ △QRM (by RHS)

Therefore ∠Q = ∠R (c.p.c.t),

$\Rightarrow$ PQ = PR (sides opposite to equal angles).

Similarly, △PQN ≅ △PQL by RHS,

Therefore ∠Q = ∠P (c.p.c.t),

$\Rightarrow$ PR = QR (sides opposite to equal angles).

Hence PQ = PR = QR
The triangle is equilateral.