Question

QS bisects angle PQR. T is a point in the interior of angle PQS. Prove that angle TQS = 1/2(TQR - PQT). (a) True (b) False

Answer 1

To prove angle TQS is equal to half of the difference between angle TQR and angle PQT, we can use the angle bisector theorem and the given ratios of segments. The statement is true.

Step-by-step explanation:

To prove that angle TQS is equal to half of the difference between angle TQR and angle PQT, we can use the angle bisector theorem. Let's start by labeling the angles and the given points. Angle PQR is bisected by QS, so we have angle PQS and angle SQR. We also have point T in the interior of angle PQS.

From the angle bisector theorem, we know that the ratio of the length of the segment QT to QS is equal to the ratio of the length of the segment PT to PS. Let's call this ratio x.

Using this information, we can set up the equation x = PT/PS = QT/QS.

Now, let's write the equation using the given angles:

1. x = PT/PS = QT/QS
2. x = PT/PS
3. x = (TQR - PQT) / (SQR)
4. Therefore, angle TQS = (TQR - PQT) / (2)

So, the statement is true, angle TQS is equal to half of the difference between angle TQR and angle PQT.

Learn more about Angle Bisector Theorem