Question

Which of the following verifies that ST⎯⎯⎯⎯⎯∥QR⎯⎯⎯⎯⎯?

Answer 1

Answer:

PS/SQ = 7.5/12.5 = 35,  PT/TR = 4.5/7.5 = 35 Since PS/SQ = PT/TR,  ST¯¯¯¯¯∥QR¯¯¯¯¯ by the Converse of the Triangle Proportionality Theorem. (The very first answer on the first page).

Step-by-step explanation:

According to the Converse of the Triangle Proportionality Theorem, if a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Find the ratio of the lengths of the line segments around point T

PTTR=4.57.5

Simplify the fraction:

PTTR=35

Therefore, PTTR=35

Find the ratio of the lengths of the line segments around point S

PSSQ=7.512.5

Simplify the fraction:

PSSQ=35

Therefore, PSSQ=35

So, PTTR=PSSQ

Since the ratios are proportional, ST¯¯¯¯¯∥QR¯¯¯¯¯

by the Converse of the Triangle Proportionality Theorem.