Question

look at the figure shown below. 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? (x + 24)/3x = 85/51 (x + 24)/85 = 51/3x (x + 24)/51 = 3x/85 34/24 = 3x/51

Explanation:

Step1: Identify corresponding sides

Since \(\triangle SPT\sim\triangle QPR\), the ratio of corresponding sides is equal. The corresponding - side pairs are \(\frac{SP}{QP}=\frac{PT}{PR}\). Here, \(SP = 3x\), \(QP=x + 24\), \(PT = 51\), and \(PR=85\).

Step2: Set up proportion equation

According to the property that corresponding sides of similar triangles are in proportion, we have \(\frac{3x}{x + 24}=\frac{51}{85}\). Cross - multiplying gives \((x + 24)\times51=3x\times85\).

Answer:

\((x + 24)\times51=3x\times85\)