Look at the figure shown below:…

Maths Questions

Look at the figure shown below: A triangle RPQ is depicted. Point S is located on side PQ, and point T is on side PR. Points S and T are connected by a straight line. The lengths are as follows: PS = 3x, SQ = 24, PT = 51, and TR = 34. Dora is writing statements to prove that if segment ST is parallel to segment RQ, then x = 12. The statements are: 1. Segment ST is parallel to segment RQ. (Given) 2. Angle QRT is congruent to angle STP because corresponding angles formed by parallel lines and their transversal are congruent. 3. Angle SPT is congruent to angle QPR due to the reflexive property of angles. 4. Triangle SPT is similar to triangle QPR, from the Angle-Angle Similarity Postulate. 5. ? Corresponding sides of similar triangles are in proportion. Which equation can she use as statement 5? a) (3x + 24):3x = 85:51 b) (3x + 24):85 = 3x:51 c) (3x + 24):51 = 3x:85 d) 34:24 = 3x:51

Answer

(A)Detailed explanation: The Postulate asserts that the sides of similar triangles maintain a proportional relationship. It’s important to note that similar triangles are those that have congruent angles, and their corresponding sides are proportional. In triangles ŒîSTP and ŒîRPQ, the correspondence of the sides is as follows: (RP, TP); (RQ, TS); (PQ, PS). Therefore, we have RP:TP = PQ:PS, which translates to 51:85 and 3x:(3x + 24). We can state this as PQ : PS = RP : TP, leading to (3x + 24):3x = 85:51. Thus, statement 5 corresponds to equation (A).

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