Question

In the adjoining figure, seg PS ⊥ side QR.

If PQ = a, PR = b, QS = c and RS = d then

complete the following activity to prove

that (a + b) (a – b) = (c + d) (c – d)

Proof In PSQ, PSQ = 900​

Answer 1

Step-by-step explanation:

In Right Δ P SQ

P Q²= PS² + SQ²→→[By Pythagoras theorem]

a²= PS² + c²

→PS² = a² - c²-------(1)

In Right Δ P SR

PR²= PS² + SR²→→[By Pythagoras theorem]

b²= PS² + d²

PS²= b² - d² ------(2)

From (1) and (2)

b²- d²= a² - c²

a² - b²= c² - d²

(a -b)(a+b)= (c-d)(c+d)→→Using the identity, A²-B²= (A-B)(A+B)

Hence proved.