In the givernAF-4AD2-3AC2.fgure, ABC is a right trangle, right angled

1.	In the givernAF-4AD2-3AC2.fgure, ABC is a right trangle, right angled at C and D is the mid-pount of BC. Prove that
Answer» ABC is a right angled at B and D is the midpoint of BC. In ∆ABD AD²= AB²+BD²…………(1)[By Pythagoras theorem] In ∆ ABCAC²= AB²+BC²…………(2) From equation (1) AD²= AB²+ (BC/2)²[D is the midpoint of BC] AD²= AB²+ BC²/4AD²= AB²/1+ BC²/44AD²= 4AB²+ BC²BC²= 4AD²-4AB²…………….(3)Using the value of BC² in eq. 2 AC²=AB²+4AD²-4AB² AC²=AB²-4AB+4AD²AC²= 4AD²-3AB²

In the givernAF-4AD2-3AC2.fgure, ABC is a right trangle, right angled at C and D is the mid-pount of BC. Prove that

Answer»

ABC is a right angled at B and D is the midpoint of BC.

In ∆ABD

AD²= AB²+BD²…………(1)[By Pythagoras theorem]

In ∆ ABCAC²= AB²+BC²…………(2)

From equation (1)

AD²= AB²+ (BC/2)²[D is the midpoint of BC]

AD²= AB²+ BC²/4AD²= AB²/1+ BC²/44AD²= 4AB²+ BC²BC²= 4AD²-4AB²…………….(3)Using the value of BC² in eq. 2

AC²=AB²+4AD²-4AB²

AC²=AB²-4AB+4AD²AC²= 4AD²-3AB²