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3 years ago

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

Mathematics

2 answers:

Goryan [66]3 years ago

7 0

Answer:

28:35

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.

yulyashka [42]3 years ago

3 0

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

$\dfrac{PQ}{PS}=\dfrac{PR}{PT}\\\\\\\Rightarrow \dfrac{2x+28}{28}=\dfrac{35+60}{35}\\\\\\\Rightarrow \dfrac{2x+28}{28}=\dfrac{95}{35}\\\\\\\Rightarrow \dfrac{2x+28}{95}=\dfrac{28}{35}\\\\\\\Rightarrow (2x+28):95=28:35.$

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

Option (B) is correct.

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