$$
\mathrm{ABC} \text { is an isosceles triangle right angled at } \mathrm{C} \text { . Prove that } \mathrm{AB}^{2}=2 \mathrm{AC}^{2} \text { . }
$$

Answer

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Geometry

NCERT Class 10 - Math

Chapter 6

Triangles

Section 5

Areas of Similar Triangles

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Video Transcript

So in the given question, we are told that there is a triangle abc such that it is an isosceles triangle, right? So let's assume that the triangle abc. Yes, sir, we are told that abc is an ISIS or strangle a right angled isosceles strangle right? And we are told to prove that a B squared is equal to two times a C squared, right? So what we can do over here is to prove this, we should take the triangle as mm B and C. Right says that A B. Is the high Putin's of the right triangle. So why we take it like this is we have a theory in called the pythagoras theorem. Right. And what does the pythagoras theorem say? So, according to the pythagoras theorem, the high part News squared the high partners. The length of the hyperthermia squared is equal to the sum of square star. It's going myself the other two sides. The other two sides, yeah. Of a triangle. Right? And this is only for a right triangle, right? So in all right. And uh right angled triangle, we can see that high powered news squared is equal to the sum of squares of the other two sides. Right, sum of squares of the lengths of the other two sides. Right? So that's what we mean. So what we can take over here is here we have the high powered news as a B. Right? So then let's take a B has the has the hyper news and we would have a B squared is equal to a C squared plus B C squared. So we are told that two of the sites of this right rangel is equal, which means we can say A C is equal to B C. And if that's the case, we can write B C, A C is the same as busy. Right? So instead of B C, we can write a C. So a C squared plus a C squared, or give us a b squared as equal to two times a C squared. So this is what we needed to show in this question. I hope you understood the answer. Thank you.

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