(05.01 LC)

Look at the figure shown below:

A triangle RPQ is shown. S is a point on side PQ and T is a point on side PR. Points S and T are joined using a straight line. The length of PS is equal to 28, the length of SQ is equal to 2x, the length of PT is equal to 35 and the length of TR is e

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 congruent 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? (1 point)

28:95

28:35

60:95

60:35

Since Rita is trying to prove that the two triangles are similar, she will be looking for corresponding sets of sides that have an equivalent ratio. Therefore, since for the big triangle she uses sides PQ and PR, the corresponding sides on the smaller triangle would be PS and PT, which have a ratio of 28:35. Hope this helps!

Answer Link

ayoushivt ayoushivt · Answer 2 · 2022-07-22T07:23:27+02:00

The statement is completed by 28 :35, the correct option is B.

What are Similar Triangles?

Two triangles of the same shape are said to be similar when their corresponding sides are proportional.

The triangle RPQ

The length of PS is equal to 28

The length of SQ is equal to 2x

The length of PT is equal to 35

The length of TR is equal to 60

The triangles SPT and QPR are proved to be similar in Step 4 by the property that corresponding sides of similar triangles are in proportion.

(2x + 28):95 =28 :35

Therefore, the statement is completed by 28 :35, the correct option is B.

To know more about Similar Triangles

https://brainly.com/question/25882965

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