Consider the diagram. which line segment has the same measure as tq. sr tr st qs

First assume that O be the point where the line segment ST and QR intersect  eachother.

Given

with the help of the diagram

OQ = OR

∠QOT = ∠TOR =∠ ROS = ∠SOQ = 90°

First prove that ΔTOQ and Δ TOR is congurent triangle.

in Δ TOQ and ΔTOR

(1) QO = OR  (As given in the diagram )

(2) ∠ TOQ = ∠TOR = 90°

(3)  TO =TO     (Common side of both triangle)

by using the SAS congurence property

ΔTOQ ≅ ΔTOR

thus

TQ = TR

(By corresponding sides of the congurent triangle)

We get

TR is line segment has the same measure as TQ.

Hence proved

explanation:

step-by-step explanation: