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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!
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!

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TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2@dan815 @Michele_Laino @triciaal QH question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.regentsprep.org/regents/math/geometry/gp6/Lisosceles.htm

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have to consider the height of your triangle with respect to its base, namely: dw:1435251966017:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok 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
 one year ago
Best ResponseYou've already chosen the best response.0well u gotta prove the height is connected to the mid point of the base too :P

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now, 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

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2You could even use a 44590 triangle. dw:1435252159759:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now, 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
 one year ago
Best ResponseYou've already chosen the best response.0I am still so confused...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Michele_Laino I dont understand any of this...

dan815
 one year ago
Best ResponseYou've already chosen the best response.0okay here ill show u how i d do it i think this is a simple way

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have to consider the height CH of the triangle with respect to the base: dw:1435252513714:dw by hypothesis we have AC=BC, right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0step #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
 one year ago
Best ResponseYou've already chosen the best response.2yo dan, you're going to confuse her with the alpha and beta :p

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2\(\sf\alpha\) and \(\sf\beta\) are just variables used for angles, repectively called alpha and beta.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0step #3 the two triangle ACH and BCH are congruent by the criterion SAS being the side CH in common

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah.... I dont get that at all...alpha and beta?

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2\(\color{blue}{\text{Originally Posted by}}\) @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
 one year ago
Best ResponseYou've already chosen the best response.0I know, but I dont have a place to put a picture, It only allows me to submit text...

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2Maybe an attach file button?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0There 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
 one year ago
Best ResponseYou've already chosen the best response.0step #4 in particular angles CAH and CBH are congruent each other dw:1435252914983:dw

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2Ok, let me try to explain to you what Dan said as the Alpha and Beta confused you.

dan815
 one year ago
Best ResponseYou've already chosen the best response.0use my proof its nice :) no theorems needed

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2dw:1435252952954:dw

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2So we have a triangle. Do you understand up until here?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes I understand that we have a triangle

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2Ok, have you learned what reflection is in math?

dan815
 one year ago
Best ResponseYou've already chosen the best response.0ok well thats not true I used the SSS theorem xD

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2so lets reflect this triangle that we have along our imaginary xaxis dw:1435253100351:dw

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2So now lets put these two triangles together and combine them:

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2dw:1435253288145:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so how does this help prove that the base angles are congruent?

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2so lets put values for our sides

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2dw:1435253562066:dw

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2so that means: dw:1435253593981:dw

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2you 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
 one year ago
Best ResponseYou've already chosen the best response.0I dont understand that....

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2dw:1435253906377:dw

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2dw:1435253954503:dw

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2This website also has another way to explain it: http://www.basicmathematics.com/baseanglestheorem.html

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Omg that other website helps me so much! Thank you so much

TheSmartOne
 one year ago
Best ResponseYou've already chosen the best response.2haha, no problem :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I guess im going to close this question now, so again, thank you so much for all of your help!!!!! :) <3
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