Question

Look at the figure shown below: A triangle RPQ is shown.

Rita is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 24.
Statement Reason
1. Segment ST is parallel to segment QR Given

2. Angle QRT is congruent to angle STP Corresponding angles formed by parallel
lines and their transversal are congruent

3. Angle SPT is congruent to angle QPR Reflexive property of angles

4.Triangle SPT is similar to triangle QPR Angle-Angle Similarity Postulate

5.(2x + 28):95 = Corresponding sides of similar triangles
are in proportion

Which of the following can she use to complete statement 5?
28:95
28:35
60:95
60:35

Answer 1

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

`(PQ)/(PS)=(PR)/(PT)\\\\\\\Rightarrow (2x+28)/(28)=(35+60)/(35)\\\\\\\Rightarrow (2x+28)/(28)=(95)/(35)\\\\\\\Rightarrow (2x+28)/(95)=(28)/(35)\\\\\\\Rightarrow (2x+28):95=28:35.`

Thus, Rita can use the proportion 28 : 35 to complete statement 5.

Option (B) is correct.

Answer 2

28:35

Step-by-step explanation:

Given the reason for step 5, Corresponding sides of similar triangles are in proportion, we are looking for sides that will be corresponding to 2x+28 and 95. 2x+28 is the length of QP and 95 is the length of PR. The matching option in our list is 28:95, because 28 is the length of SP and 35 is the length of PT.