(1) In the figure, seg PS i side QRthen prove thata+ba-b) (c +d)c-d.

1.	(1) In the figure, seg PS i side QRthen prove thata+ba-b) (c +d)c-d.
Answer» 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.

Answer»

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.

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