Question

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 3x, the length of SQ is equal to 24, the length of PT is equal to 51 and the length of TR is equal to 34. Dora is writing statements as shown below to prove that if segment ST is parallel to segment RQ, then x = 12: 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. ? Corresponding sides of similar triangles are in proportion. Which equation can she use as statement 5? (3x + 24):3x = 85:51 (3x + 24):85 = 3x:51 (3x + 24):51 = 3x:85 34:24 = 3x:51

Answer 1

Answer: A) (3x + 24):3x = 85:51

Answer 2

(A)

Explanation:

The Postulate states that corresponding sides of similar triangles are in proportion.

We know that similar triangles are the triangle which have congruent triangles and and the corresponding sides are in proportion

Now in ΔSTP and ΔRPQ, corresponding sides are : (RP,TP); (RQ,TS) ; (PQ,PS)

So we have RP:TP = PQ:PS

TP= 51; RP= 85; PS = 3x; PQ = 3x+24

PQ : PS = RP : TP

3x+24 : 3x = 85 : 51

Hence 5 statement represents (A) equation