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

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)

 (Radius of the circle are equal and congruent in length)

 (Radius of the circle)

∴ ΔPTQ ≅ ΔSTR (SAS postulate)

∴ (corresponding sides of congruent triangle are equal  and congruent).

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