**S Chand ICSE Mathematics Class 9 Solution Tenth Chapter Pythagoras Theorem Exercise 10B**

**(1) ABCD is a square, prove that AC ^{2} = 2AB^{2}**

**(2) In Fig. 10.26, AB = BC = CA = 2a and segment AD ⊥ side BC, Show that**

**(i) AD = a √3, (ii) area of ΔABC = a ^{2}√3**

**Solution: **

**(3) In Fig 10.27, prove that AB ^{2} – AD^{2} = CD^{2} – CB^{2},**

**(4) In a ΔABC, AD ⊥ BC, Prove that:**

**AB ^{2} + CD^{2} = AC^{2} + BD^{2}.**

**(5) In a quadrilateral ABCD, the diagonals AC, BD intersect at right angles. Prove that:**

**AB ^{2} + CD^{2} = BC^{2} + DA^{2}.**

**Solution: **

**(6) In ΔABC, ∠B = 90 ^{o} and D is the mid point of BC, Prove that**

**(i) AC ^{2} = AD^{2} + 3CD^{2} (ii) BC^{2} = 4(AD^{2} – AB^{2})**

**Solution: **