Its very important question of chapter triangles ncert class 9th . Find the best and simplest solution of exercise 7.2 question 6 ,Please help me to solve this question in a best and simplest way.ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that BCD is a right angle.

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# ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that BCD is a right angle.Q.6

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It is given that AB = AC and AD = AB

We will have to now prove BCD is a right angle.

Proof:Consider ΔABC,

AB = AC (It is given in the question)

Also, ACB = ABC (They are angles opposite to the equal sides and so, they are equal)

Now, consider ΔACD,

AD = AB

Also, ADC = ACD (They are angles opposite to the equal sides and so, they are equal)

Now,

In ΔABC,

CAB + ACB + ABC = 180°

So, CAB + 2ACB = 180°

⇒ CAB = 180° – 2ACB — (i)

Similarly, in ΔADC,

CAD = 180° – 2ACD — (ii)

also,

CAB + CAD = 180° (BD is a straight line.)

Adding (i) and (ii) we get,

CAB + CAD = 180° – 2ACB+180° – 2ACD

⇒ 180° = 360° – 2ACB-2ACD

⇒ 2(ACB+ACD) = 180°

⇒ BCD = 90°