Question

QTR is a right triangle TQR is a right triangle QS is an altitude which statements are true

Answer 1

Answer:

(TQ)² + (QR)² = (ST) (QS) + (SR) (QS)

Step-by-step explanation:

PROOF:

QTR is a right triangle TQR is a right triangle QS is an altitude

From right angle theorem

Side √TQ² = √(QS² + ST²) reason ∠QST is right angled

Side √QR² = √(SR² + QS²) reason ∠RSQ is right angled

QED

Answer 2

Answer:

4)

$(TQ)^2+(QR)^2=(ST)(TR)+(SR)(TR)$

Explanation:

$m\angle QTR=m\angle SQR\\m\angle TSQ=m\angle TQR=90°\\\implies \Delta TSQ \sim \Delta TQR\\\implies \frac{TQ}{TR}=\frac{TS}{TQ}\\\implies \boxed{(TQ)^2= (TS)(TR)}\\\text{Similarly, use triangles RSQ and RQT to get:}\\\boxed{(QR)^2=(SR)(TR)}$

Now add the two equations to get the answer.