Points O, P, and Q are not collinear and form ∠POQ. Point R is on OP−→− between points O and P. Line l passes through R parallel to PQ¯¯¯¯¯¯¯¯. Line l intersects OQ−→− at point S. Use paper to draw a diagram to represent the situation described. Which other pairs of segments have lengths in the same ratio as RS to PQ? Select all that apply.

The answer is below

Explanation:

Two triangles are said to be similar to each other if the ratio of their corresponding sides are in the same proportion.

Given triangle ORS and triangle OPQ. ∠ROS = ∠POQ

∠ORS = ∠OPQ (corresponding angles are equal). Also, ∠OSR = ∠OQP (corresponding angles are equal)

Therefore using angle angle similarity theorem, we can say triangle ORS is similar to triangle OPQ.

Therefore:

ratio of RS to PQ = ratio of OR to OP = ratio of OS to OQ  

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