Question

class 9 ex 8.1 q8
pls help me with this sum

Answer 1

Answer :


ABCD is a rectangle.

AB = DC

BC = AD -------- (1)

Also each angle ;

angle A = angle B = angle C = angle D = 90°


(i) In ∆s ABC and ABC,

angle 1 = angle 2

angle 3 = angle 4

【 AC bisects angle A and angle C given】



AC = AC 【 Common 】

Therefore By ASA congurence,

∆ABC = ∆ADC


Therefore, AB = AD ------- (2)


From (1) and (2),

AB = BC = AD = DC.

All sides of a rectangle are equal.

Hence, it is a square.

(ii) In ∆s ABD and BDC,

AB = BC,

【 Rectangle ABCD is a square proved in part (¡)】


AD = DC 【 ABCD is a square】

BD = BD. 【Common】


Therefore by SSS Congurence,


∆ABD = ∆CBD

Therefore,

angle ABD = angle CBD ----- (3)

angle ADB = angle CDB ---- (4)


(3) and (4) imply that diagonal BD bisects both angle B and angle D.






HOPE IT WOULD HELP YOU

Answer 2

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$\huge \bold \color {brown} {In \: Attachment}$

For 1st Part :- Figure 1

For 2nd part - figure 2