## anonymous one year ago Prove that the base angles of an isosceles triangle are congruent. Be sure to create and name the appropriate geometric figures. I really need to pass this class! So any help would be amazing!

1. TheSmartOne

@dan815 @Michele_Laino @triciaal QH question

2. anonymous
3. Michele_Laino

we have to consider the height of your triangle with respect to its base, namely: |dw:1435251966017:dw|

4. anonymous

Ok but If I have to show this in text, because I cannot post pictures. So if i had to type out an explanation how would I do that?

5. dan815

well u gotta prove the height is connected to the mid point of the base too :P

6. Michele_Laino

now, there exists a theorem which states that for an isosceles triangle the heigh with respect to its base is also a median of its base and bisects the angle at vertex C. In other words the angles ACH and BCH are congruent, and AH is congruent to BH |dw:1435252103138:dw|

7. dan815

|dw:1435252124559:dw|

8. TheSmartOne

You could even use a 4-45-90 triangle. |dw:1435252159759:dw|

9. TheSmartOne

45-45-90 **

10. Michele_Laino

now, using the criterion SAS we can states that the two triangles ACH and BCH are congruents each other, in particular the two angles CAH and CBH are congruent each other

11. anonymous

I am still so confused...

12. anonymous

@Michele_Laino I dont understand any of this...

13. dan815

okay here ill show u how i d do it i think this is a simple way

14. dan815

|dw:1435252537882:dw|

15. Michele_Laino

we have to consider the height CH of the triangle with respect to the base: |dw:1435252513714:dw| by hypothesis we have AC=BC, right?

16. dan815

|dw:1435252556250:dw|

17. Michele_Laino

step #2 exixts a theorem which states that the height CH is also the bisector of the angle ACB: |dw:1435252664811:dw| so the angles ACH and BCH are congruent each other

18. TheSmartOne

yo dan, you're going to confuse her with the alpha and beta :p

19. TheSmartOne

$$\sf\alpha$$ and $$\sf\beta$$ are just variables used for angles, repectively called alpha and beta.

20. Michele_Laino

step #3 the two triangle ACH and BCH are congruent by the criterion SAS being the side CH in common

21. Michele_Laino

triangles*

22. anonymous

Yeah.... I dont get that at all...alpha and beta?

23. TheSmartOne

$$\color{blue}{\text{Originally Posted by}}$$ @camzzz12 Ok but If I have to show this in text, because I cannot post pictures. So if i had to type out an explanation how would I do that? $$\color{blue}{\text{End of Quote}}$$ Your question states: "Be sure to create and name the appropriate geometric figures."

24. anonymous

I know, but I dont have a place to put a picture, It only allows me to submit text...

25. TheSmartOne

Maybe an attach file button?

26. anonymous

There is none, I looked for it before but I dont see one. All that there is, is a text box and the question

27. Michele_Laino

step #4 in particular angles CAH and CBH are congruent each other |dw:1435252914983:dw|

28. TheSmartOne

Ok, let me try to explain to you what Dan said as the Alpha and Beta confused you.

29. anonymous

30. dan815

use my proof its nice :) no theorems needed

31. TheSmartOne

|dw:1435252952954:dw|

32. TheSmartOne

So we have a triangle. Do you understand up until here?

33. anonymous

Yes I understand that we have a triangle

34. TheSmartOne

Ok, have you learned what reflection is in math?

35. dan815

ok well thats not true I used the SSS theorem xD

36. anonymous

Yes

37. TheSmartOne

so lets reflect this triangle that we have along our imaginary x-axis |dw:1435253100351:dw|

38. TheSmartOne

still with me?

39. anonymous

yes

40. TheSmartOne

So now lets put these two triangles together and combine them:

41. TheSmartOne

|dw:1435253288145:dw|

42. anonymous

ok so how does this help prove that the base angles are congruent?

43. TheSmartOne

so lets put values for our sides

44. TheSmartOne

|dw:1435253562066:dw|

45. TheSmartOne

so that means: |dw:1435253593981:dw|

46. TheSmartOne

you can see that if you look at one triangle at a time that the angle 60 has a side length of √3 if you look at the whole triangle as a whole, you can see that the two angle 60 has a side length of 2

47. anonymous

I dont understand that....

48. TheSmartOne

|dw:1435253906377:dw|

49. TheSmartOne

|dw:1435253954503:dw|

50. TheSmartOne

This website also has another way to explain it: http://www.basic-mathematics.com/base-angles-theorem.html

51. anonymous

Omg that other website helps me so much! Thank you so much

52. TheSmartOne

haha, no problem :)

53. anonymous

I guess im going to close this question now, so again, thank you so much for all of your help!!!!! :) <3

54. TheSmartOne

Anytime :)