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

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).