# I have to prove a triangle is Isosceles. After I say what each symbol and side is, how do I say it is Isosceles.Can I puit its Isosceles because it has 2 angles are congruent or how I have it? Is...

I have to prove a triangle is Isosceles. After I say what each symbol and side is, how do I say it is Isosceles.

Can I puit its Isosceles because it has 2 angles are congruent or how I have it? Is that the right reason?

They are right angles because the

┴ means the 2 segments are perpendicular

Reflexive property- shared side

CPCTC-Corresponding parts of congruent triangles are congruent.

ASA-If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

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### 2 Answers

i made a mistake in the above solution,

the the angle should be A=120 , B=30 and C=30 as the sum of the three angles of the triangle should be always 180.

so

n ADB,

sin 30 = AD/AB

and in ADC

sin 30 = AD/AC,

so

AD/AB = AD/AC = sin 30

this is possible only when AB = AC as AD is common.

so the triangle is Isoscele

do let me know if you have any doubts.... I would be more than happy to help you out..

If I understood your question, you mean to say how to proove a triangle whether it is Isosceles or not.

We cannot apply CPCTC as we would need another triangle for it to do.

Now if a triangle is Isosceles, then the corresponding angle has to be equal. if you can porve it then it is done.

Now in case of right angled triangle, we can used the trigonometric ratio.

Now let us consider the angles to be 45,45 and 90

tan 45 = adjacent/base and cot 45 = base/adjacent

tan 45 = cot 45=1

adjacent/base = base/adjacent = 1

that is base = adjacent

so the trinagle is Isoscele

Now lets take another example, triangle ABC, were angle A=120 , B=60 and C=60

for this we need to pove AB= AC {Isoscele}

now draw a perpendicular line form A so that it meets BC at D.

Now ADB and ADC are right angled triangle, were angle D= 90,

here apply sine ratio

in ADB,

sin 60 = AD/AB

and in ADC

sin 60 = AD/AC,

so

AD/AB = AD/AC = sin 60

this is possible only when AB = AC as AD is common.

so the triangle is Isoscele

[it would have been better if I could post the daigram, but I cant.. please feel free to clear you doubt if you have any..]