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Question
Construct a right-angled triangle in which: QP = QR and hypotenuse PR = 7 cm
Solution
In ΔPQR,
QP = QR ....(given)
⇒ ∠QPR = ∠QRP ....
Since hypotenuse PR = 7cm, ∠PQR = 90°
∴ ∠QPR + ∠QRP = 90°
⇒ ∠QPR = ∠QRP = 45°
Steps:
1. Draw PR = 7cm.
2. Draw a ray PT such as ∠RPT = 45° and ray RS such as ∠PRS = 45°
3. Ray RS and ray PT meets at Q.
Thus, PQR is the required triangle.
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