anonymous
  • anonymous
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!
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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TheSmartOne
  • TheSmartOne
@dan815 @Michele_Laino @triciaal QH question
anonymous
  • anonymous
http://www.regentsprep.org/regents/math/geometry/gp6/Lisosceles.htm
Michele_Laino
  • Michele_Laino
we have to consider the height of your triangle with respect to its base, namely: |dw:1435251966017:dw|

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anonymous
  • 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?
dan815
  • dan815
well u gotta prove the height is connected to the mid point of the base too :P
Michele_Laino
  • 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|
dan815
  • dan815
|dw:1435252124559:dw|
TheSmartOne
  • TheSmartOne
You could even use a 4-45-90 triangle. |dw:1435252159759:dw|
TheSmartOne
  • TheSmartOne
45-45-90 **
Michele_Laino
  • 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
anonymous
  • anonymous
I am still so confused...
anonymous
  • anonymous
@Michele_Laino I dont understand any of this...
dan815
  • dan815
okay here ill show u how i d do it i think this is a simple way
dan815
  • dan815
|dw:1435252537882:dw|
Michele_Laino
  • 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?
dan815
  • dan815
|dw:1435252556250:dw|
Michele_Laino
  • 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
TheSmartOne
  • TheSmartOne
yo dan, you're going to confuse her with the alpha and beta :p
TheSmartOne
  • TheSmartOne
\(\sf\alpha\) and \(\sf\beta\) are just variables used for angles, repectively called alpha and beta.
Michele_Laino
  • Michele_Laino
step #3 the two triangle ACH and BCH are congruent by the criterion SAS being the side CH in common
Michele_Laino
  • Michele_Laino
triangles*
anonymous
  • anonymous
Yeah.... I dont get that at all...alpha and beta?
TheSmartOne
  • 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."
anonymous
  • anonymous
I know, but I dont have a place to put a picture, It only allows me to submit text...
TheSmartOne
  • TheSmartOne
Maybe an attach file button?
anonymous
  • 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
Michele_Laino
  • Michele_Laino
step #4 in particular angles CAH and CBH are congruent each other |dw:1435252914983:dw|
TheSmartOne
  • TheSmartOne
Ok, let me try to explain to you what Dan said as the Alpha and Beta confused you.
anonymous
  • anonymous
Please do...
dan815
  • dan815
use my proof its nice :) no theorems needed
TheSmartOne
  • TheSmartOne
|dw:1435252952954:dw|
TheSmartOne
  • TheSmartOne
So we have a triangle. Do you understand up until here?
anonymous
  • anonymous
Yes I understand that we have a triangle
TheSmartOne
  • TheSmartOne
Ok, have you learned what reflection is in math?
dan815
  • dan815
ok well thats not true I used the SSS theorem xD
anonymous
  • anonymous
Yes
TheSmartOne
  • TheSmartOne
so lets reflect this triangle that we have along our imaginary x-axis |dw:1435253100351:dw|
TheSmartOne
  • TheSmartOne
still with me?
anonymous
  • anonymous
yes
TheSmartOne
  • TheSmartOne
So now lets put these two triangles together and combine them:
TheSmartOne
  • TheSmartOne
|dw:1435253288145:dw|
anonymous
  • anonymous
ok so how does this help prove that the base angles are congruent?
TheSmartOne
  • TheSmartOne
so lets put values for our sides
TheSmartOne
  • TheSmartOne
|dw:1435253562066:dw|
TheSmartOne
  • TheSmartOne
so that means: |dw:1435253593981:dw|
TheSmartOne
  • 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
anonymous
  • anonymous
I dont understand that....
TheSmartOne
  • TheSmartOne
|dw:1435253906377:dw|
TheSmartOne
  • TheSmartOne
|dw:1435253954503:dw|
TheSmartOne
  • TheSmartOne
This website also has another way to explain it: http://www.basic-mathematics.com/base-angles-theorem.html
anonymous
  • anonymous
Omg that other website helps me so much! Thank you so much
TheSmartOne
  • TheSmartOne
haha, no problem :)
anonymous
  • anonymous
I guess im going to close this question now, so again, thank you so much for all of your help!!!!! :) <3
TheSmartOne
  • TheSmartOne
Anytime :)

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