Question

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. Corresponding sides of similar triangles are in proportion. Which equation can she use as statement 5?
x:15 = 28:40

28:12 = x:(x + 15 )

x + 15 = 28 + 12

28:40 = x:(x + 15)

Answer 1

Option IV is the right answer

Explanation:

Similar triangles will have all angles congruent and corresponding sides will be proportional

Given x=35 let us check one by one option whether right or not

Option I:

Left side = x:15 =35:15 =7:3. But right side = 28:40 =7:10 Hence not correct

Option II:

Left side =28:12 =7:3. But right side = 35:50 =7:10 Hence not correct

Option III:

Left side = x+15 =35+15 =50. But right side = 28+12=40 Hence not correct

Option IV:

Left side = 28:40 =7:10 And right side =x:x+15=35:50=7:10 Hence correct

Answer 2

Given that x = 35
35 : 15 ≠ 28 : 40

28 : 12 ≠ 35 : (35 + 15)

35 + 15 ≠ 28 + 12

28 : 40 = 35 : (35 + 15)
7 : 10 = 35 : 50
7 : 10 = 7 : 10

Therefore, the last option is the answer.