## anonymous one year ago Several triangles are shown below with congruent sides, congruent angles and right angles shown. NEED HELP PLEASE!!! I WILL GIVE YOU A MEDAL IF YOU ANSWER.

1. anonymous

2. mathstudent55

What is a scalene triangle?

3. anonymous

A triangle that are unequal.

4. anonymous

kind of like this

5. mathstudent55

Yes, all sides have different lengths.

6. anonymous

|dw:1435628118651:dw|

7. mathstudent55

I think you can only conclude two sides are congruent if the figure shows it, right? For example in triangle ABC, we are shown that sides AB and BC are congruent.

8. mathstudent55

In triangle FED, we don't know that any sides are congruent.

9. anonymous

I got for A. QRT DEF, and GHI

10. anonymous

so it would only be QRT?

11. mathstudent55

|dw:1435628307134:dw|

12. mathstudent55

We only know about sides being congruent in the three triangles on the left. That means the three triangles on the right are scalene.

13. mathstudent55

|dw:1435628565788:dw|

14. mathstudent55

(a) Triangles FED, JKL, and QRT

15. anonymous

ok thanks

16. mathstudent55

Ok. Now isosceles. What is an isosceles triangle?

17. anonymous

|dw:1435628698681:dw|

18. mathstudent55

Can you explain it in words? What do you know about lengths of sides in an isosceles triangle?

19. anonymous

Umm, its kind of elongated in a way.

20. mathstudent55

Specifically, an isosceles triangle is a triangle that has at least two congruent sides.

21. mathstudent55

Examples of isosceles triangle. In each case, at least two sides are congruent. |dw:1435628860898:dw|

22. mathstudent55

If all sides are congruent, then it's a special case of an isosceles triangle that is also equilateral.

23. mathstudent55

Now look in the figure of your problem. Which triangles have at least two congruent sides?

24. anonymous

GHI, AND ABC

25. mathstudent55

|dw:1435628996774:dw|

26. mathstudent55

Also MNP

27. mathstudent55

(b) Triangles ABC, GHI, MNP

28. anonymous

But its right? how does it have same sides?

29. mathstudent55

You mean MNP?

30. anonymous

yes

31. mathstudent55

The figure with your problem shows little marks on the sides of triangle MNP . Those marks mean that those sides are congruent.

32. anonymous

oh ok thanks

33. mathstudent55

|dw:1435629184547:dw|

34. mathstudent55

Ok, next is (c). Which triangles are right triangles? A right triangle has one right angle.

35. anonymous

MNP AND DEF?

36. mathstudent55

|dw:1435629246793:dw|

37. mathstudent55

Correct. (c) Triangles EDF and MNP

38. mathstudent55

Now (d), equilateral triangles. An equilateral has all three sides congruent.

39. anonymous

ABC, JKL

40. mathstudent55

In triangle ABC, we only know sides AB and BC are congruent. That makes the triangle isosceles. To be equilateral, you need all sides congruent. The sides of triangle JKL have no marks on them at all. We don't know what their lengths are and if they are the same or different. Therefore, we cannot make any conclusions about the sides being congruent. Look at triangle GHI. The 2 marks on each side mean that all sides are congruent. Triangle GHI is equilateral.

41. mathstudent55

(d) Triangle GHI

42. anonymous

is there a difference betwen the lines on ABC and GHI

43. anonymous

?

44. mathstudent55

In ABC, two sides have 1 mark each. That means those two sides are congruent. In GHI, each side has two marks each. That means all three sides are congruent, but different from the sides in ABC.

45. anonymous

aww ok

46. mathstudent55

On the other hand, since sides AB and BD have one mark each, and sides MN and NP also have one mark each, that means all 4 of those sides are congruent.

47. mathstudent55

Finally, we get to (e). Do you know what an obtuse triangle is?

48. mathstudent55

(Hint: think of a right triangle, but substitute obtuse for right.)

49. anonymous

yes it means that it's greater then 90 degrees.

50. anonymous

than

51. mathstudent55

Right triangle: \(\sf A ~\color{red}{right} ~triangle ~has ~one ~\color{red}{right} ~angle.\) Obtuse triangle: \(\sf A \color{green}{n~obtuse} ~triangle ~has ~one ~\color{green}{obtuse} ~angle.\)

52. mathstudent55

Correct. Which triangles have one angle of more than 90 degrees?

53. anonymous

QRT

54. mathstudent55

Correct, but I think that JKL also has an obtuse angle. |dw:1435630158625:dw|

55. mathstudent55

(e) Triangles JKL and QRT

56. anonymous

oh ok

57. anonymous

Thank you so much for all the help I needed it!

58. mathstudent55

You are welcome.