Question

ΔPQR is isosceles with PQ = PR. T is the mid-point of QR, and TM and TN are perpendiculars on PR and PQ respectively. Prove that,
TM = TN

Answer 1

In ΔPQR,
PQ = PR   ...(given)
∴ ∠R = ∠Q .................(i)
Now in ΔQNT and ΔRMT
∠QNT =∠RMT    ...(90°)
∠Q = ∠R            ...(from (i))
QT = TR               ...(given)
∴ ΔQNT ≅ ΔRMT   ...(AAS criteria)
∴ TN = TM.