need_help! 3 years ago In triangle PQR, < PQR is right and QT is an altitude Name the three similar triangles. How do you name them?! O.o idk but I got : triangle PQT is similar to triangle PRQ triangle TQR is similar to triangle QPR triangle PQT is similar to triangle QPT ?

1. Mertsj

Need a posting that we can understand.

2. need_help!

Do you want me to draw it ?

3. Mertsj

yep

4. need_help!

Okay, I'll try.

5. need_help!

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6. Directrix

Should be a right angle at T ??

7. Mertsj

Separate the triangles and draw them all in similar position.

8. need_help!

yes @ directrix

9. need_help!

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10. Directrix

If an altitude is drawn to the hypotenuse of a right triangle, the two triangles formed are similar to each other and to the given right triangle.

11. Directrix

Triangle PQR ~ Triangle QTR ~ Triangle PTQ

12. need_help!

So, is this correct? triangle PQT is similar to triangle PRQ triangle TQR is similar to triangle QPR triangle PQT is similar to triangle QPT

13. Mertsj

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14. Mertsj

Directrix is correct.

15. Directrix

Match up right angles of all 3. Of the larger and one smaller, then match up angles they share. The 3rd pair of vertices have no place to go but to each other.

16. Directrix

@ Mert --> Right angle at T on drawing or the theorem is not valid.

17. need_help!

Wait, can you just PLEASE tell me if what I did is correct or wrong ?

18. need_help!

I think

19. Directrix

@Fool --> Valid for all right triangles satisfying the hypothesis of the theorem I wrote somewhere up this thread.

20. Directrix

triangle PQT is similar to triangle QPT --> This third section of Help's answer seems to name the same two triangles. Look at that again, Help.

21. phi

@need triangle PQT is similar to triangle QPT . this is the same triangle. The 3 are PQR, QTR, PTQ (note that you should order the vertices to show what angles (sides) are congruent)

22. need_help!

I know, I need them to be separate.. like what I did..

23. phi

*similar (not congruent!)

24. FoolForMath

So, apparently, \( \angle TQR = \angle TPQ \) hence the correspondence

25. phi

there are only 3 angles: 90, A, and (90-A), so it is easy to show similarity of triangles

26. phi

Name the three similar triangles. means write down triangle PQR, triangle QTR, triangle PTQ

27. need_help!

Yeah, kinda.. I understand how you name the big triangle with one of the small triangles but what is I dont get or don't how is how to name the small triangle with the other small triangle? & this is => triangle PQT is similar to triangle QPT wrong?

28. Directrix

Be systematic. It's easy to get confused on these. Start with the original triangle. Call it what you like. You called it PRQ, I think. State the similarity of PRQ to one of the smaller triangles, say PQT. First, match the right angles from larger triangle to smaller. Q has to match to T. They share angle P so P has to match to P. That forces R of the larger triangle to Q of the smaller. Result : Triangle PRQ ~ Triangle PQT Next, match Triangle PRQ to the other triangle keeping the same order of letters, PRQ. Then, the two smaller triangle will be similar to each other by the transitive property.

29. need_help!

Aooh! So, what I did is correct?! :D

30. phi

you name a triangle by listing its vertices.

31. need_help!

really? -.- what is triangle PQT similar to?

32. phi

what is triangle PQT similar to? triangle PRQ and triangle QTR

33. need_help!

Why not PRQ with QRT ?

34. need_help!

or same thing?

35. phi

triangle QTR is the same as QRT. (same points). But if I did it write, when we ask what is triangle PQT similar to, the P corresponds to Q, the Q to T, and the T to R

36. phi

*write -> right i.e. correctly

37. Directrix

I was trying to teach you how to do this but so many people have posted so much stuff that I have lost track. This is the way I do these problems: Be systematic. It's easy to get confused on these. Start with the original triangle. Call it what you like. You called it PRQ, I think. State the similarity of PRQ to one of the smaller triangles, say PQT. First, match the right angles from larger triangle to smaller. Q has to match to T. They share angle P so P has to match to P. That forces R of the larger triangle to Q of the smaller. Result : Triangle PRQ ~ Triangle PQT Next, match Triangle PRQ to the other triangle keeping the same order of letters, PRQ. Then, the two smaller triangle will be similar to each other by the transitive property. That does not mean what you did is incorrect. As best I remember, yours were correct except for the third pair of triangles in which you listed the same triangle twice.

38. need_help!

Man! This is confusing -.- but I think I get it now.. thanks to you guys!! =D I saw where I went wrong in the last one. Thank you =))

39. phi

Labeling the angles helps. but you are right, it can get confusing

40. need_help!

Oh yeah!! i remembered something just don't know if it's right or wrong..

41. need_help!

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42. phi

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43. need_help!

sorry, the computer just froze! I was saying that these two angles are always congruent?