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 radi
i. 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
2 answers:
Answer:
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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Answer:
? = 3
Step-by-step explanation:
The parallel segments shown divide the sides in the ratio
=
( cross- multiply )
4? = 12 ( divide both sides by 4 )
? = 3