Question

Helppppp! Angles PTQ and STR are vertical angles and congruent. Circle T is shown. Line segments T P, T Q, T R, and T S are radii. Lines are drawn to connect the points on the circle and form secants P Q, Q R, R S, and S P. Angles P T Q and S T R are congruent. Which chords are congruent? QP and SR QR and PR and RS PR and PS

Answer 1

Answer:

$\overline{QP} = \overline{SR}$

Step-by-step explanation:

Given: ∠PTQ ≅ ∠STR and TP, TQ, TR and TS are radii of the circle.

If  two angle are equal, then they are equal in size and their measurements are equal.

IF ∠PTQ ≅ ∠STR then they are also equal in their measurements.

Now, In ΔPTQ and ΔSTR

∠PTQ ≅ ∠STR  (vertically opposite angle)

$\overline{TQ} \cong \overline{ST}$  (Radius of the circle are equal and congruent in length)

$\overline{PT} \cong \overline{TR}$  (Radius of the circle)

∴ ΔPTQ ≅ ΔSTR (SAS postulate)

∴ $\overline{QP}\cong \overline{SR}$ (corresponding sides of congruent triangle are equal  and congruent).

Answer 2

Answer:

QP=SR

Step-by-step explanation: