Answer: The correct option is (B) 28 : 35.
Step-by-step explanation: A triangle PQR is shown in the given figure. Rita is writing statements to prove that if segment ST is parallel to segment RQ, then x = 24.
Also, given that
PS = 28, SQ = 2x, PT = 35 and TR = 60.
We are to select the correct proportion that completes statement 5.
The statements are as follows:
(1). Given that Segment ST is parallel to segment QR.
(2). ∠QRT is congruent to ∠STP [Corresponding angles formed by parallel lines and their transversal are congruent].
(3). ∠SPT is congruent to ∠QPR [Reflexive property of angles].
(4). So, Δ SPT is similar to ΔQPR [Angle-Angle Similarity Postulate].
The next (fifth) step will be
(5) We know that the corresponding sides of similar triangles are proportional, so we must have
![\dfrac{PQ}{PS}=\dfrac{PR}{PT}\\\\\\\Rightarrow \dfrac{2x+28}{28}=\dfrac{35+60}{35}\\\\\\\Rightarrow \dfrac{2x+28}{28}=\dfrac{95}{35}\\\\\\\Rightarrow \dfrac{2x+28}{95}=\dfrac{28}{35}\\\\\\\Rightarrow (2x+28):95=28:35.](https://tex.z-dn.net/?f=%5Cdfrac%7BPQ%7D%7BPS%7D%3D%5Cdfrac%7BPR%7D%7BPT%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B2x%2B28%7D%7B28%7D%3D%5Cdfrac%7B35%2B60%7D%7B35%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B2x%2B28%7D%7B28%7D%3D%5Cdfrac%7B95%7D%7B35%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B2x%2B28%7D%7B95%7D%3D%5Cdfrac%7B28%7D%7B35%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20%282x%2B28%29%3A95%3D28%3A35.)
Thus, Rita can use the proportion 28 : 35 to complete statement 5.
Option (B) is correct.