Question

In ΔRST shown below, segment SU is an altitude:

Triangle RST with segment SU drawn from vertex S and intersecting side RT.

Which of the following is a justification used while proving the similarity of triangles ΔRUS and ΔSUT?

Transitive Property of Equality
Addition Property of Equality
Definition of Supplementary Angles
Definition of Congruence

Answer 1

@mathmale

Answer 2

@tkhunny

Answer 3

@Nnesha

Answer 4

CAN ANYONE HELP ME???? @Directrix

Answer 5

@Hero

Answer 6

Have you tried eliminating the least likely answers? have you tried looking up the meaning of all four answers to help you in this task?

I have no idea what "transitive property of equality" is, so will look it up myself.

Answer 7

What is the Definition of Congruence? Have you looked this up?

Answer 8

ok, i thought it was D

Answer 9

its when 2 angles have the same measure

Answer 10

I believe we both need to look it up. Congruence does NOT seem to apply here, because the 2 smaller triangles are not of the same size and could thus not be congruent.

Their corresponding angles are congruent (same sized), but their corresponding sides are not congruent (different lengths).

This is what I mean by "eliminate the least likely possible answers."

I would eliminate D with a good sense of certainty.

Answer 11

Think back: How have you proved "similarity" in the past? Is "similarity" the same thing as "congruence" or something different?

Answer 12

ok

Answer 13

no its different

Answer 14

its not the same but almost

Answer 15

Define "similar triangles." This would give you some criteria for determining which answer is probably right.

Right: similar does not mean congruent, altho congruent certainly does imply similar.

What is the def'n of "similar" ? of "similar triangles" ?

Answer 16

similar triangles is when points of one triangle matches the other triangles. P=P or S=S

Answer 17

I do not necessarily know the answer to this question; I'm looking into possibilities (as you also need to do). Let's not say "points of one triangle match those of the other;" instead, angles of one triangle match the corresponding angles of the other triangle.

Is that the case here?

Answer 18

yes, i have to prove the similarity

Answer 19

If the ANGLES of a given triangle math the corresponding angles of another triangle, then the 2 triangles are similar (but not necessarily congruent).

Answer 20

i think that the best answer would be A, right?

Answer 21

That's one clue to follow. Can we prove that the 3 angles of the smaller triangle are congruent with the 3 corresponding angles of the larger triangle?

Answer 22

I need for you to defend your choice of answer A.

Answer 23

ugghhh, now im confused

Answer 24

Notice that because SU is an altitude of triangle RST, SU is by definition perpendicular to side RT. This means that you have a 90 degree angle on both sides of SU where it intersects side RT. Hope this helps.

Why should you be confused? You've chosen A tentatively, and all I did was ask you to defend (explain) your choice of A.

Answer 25

Wait, so would it be A?

Answer 26

Have you a textbook? If I had one for your course, I'd review it and look for examples of each of the properties given as possible answers.

I did NOT say that it should or would be A. You chose A; I'm asking you to defend your choice.

Answer 27

What does "supplementary angles" mean?

Answer 28

supplementary angles are two angles that add up to 180

Answer 29

That would certainly be true of the 2 angles formed at point T by the altitude SU. that's one way in which you could prove that the 2 smaller triangles share at least ONE congruent angle. From the looks of the problem, and thinking about what would happen were we to rotate triangle STU about the point U, the 2 triangles are similar. But we can't go by looks alone.

Answer 30

ok, that makes a little sense

Answer 31

We know definitely that angles RUS and SUT are equal through 2 reasons (at least): One, that they are supplem. angles, and Two, that the alt. SU is perpendicular to side RT.

I truly hope this discussion has helped you. As before, I do not necessarily know the correct answer, so am trying to point out for you some relevant facts that may help you make the right choice.

I'd like to get off the 'Net. If you have no more than one question or comment, go ahead with it.

Answer 32

OKAY IM GOING TO GO WITH C, thank you

Answer 33

@anonymous223 do u know if its C?

Answer 34

@jabez1777 @zepdrix @triciaal @radar

Answer 35

FOR FUTURE PEOPLE, ITS NOT C............I DONT KNOW WHAT IT IS THOUGH