Question

Look at the figure shown below.Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.

Answer 1

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.

Answer 2

Which equation can she use as statement 5?

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

(3x + 24) : 81 = 3x : 51

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

34 : 24 = 3x : 51

Answer 3

k

Answer 4

do you understand the objective, here?

Answer 5

Well, the goal is the set up a ratio for the triangles.

Answer 6

To fill in statement 5 for the given reason.

Answer 7

k

Answer 8

hmm

Answer 9

well, we need to find out what x equals

Answer 10

Actually, no you don't

Answer 11

we need to find if x truly equals 12

Answer 12

so choice 4 is wrong

Answer 13

x=54.1875 there

Answer 14

Again, we have no need to solve for x here. The ratio of the two triangles is 85 : 51. Can you see where I got that?

Answer 15

hmmm

Answer 16

yep

Answer 17

Yeah. We're setting up a ratio for the sides of the two TRIANGLES not the two segments of a side. Knowing how I got that, can you do the same with the ide involving x without solving for x?

Answer 18

well

Answer 19

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

Answer 20

thats the only choice thats left

Answer 21

and it seems that (3x+24) is part of the bigger triangle

Answer 22

Yeah. DO you get why the 3x + 24 : 3x part is correct?

Answer 23

yep

Answer 24

good job

Answer 25

k

Answer 26

now

Answer 27

for one more problem

Answer 28

BRING IT ON! :P