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Step-by-step explanation:

c) In triangles AOC and BOD, we have

AO = BO (O, the midpoint of AB);

∠AOC=∠BOD, (vertically opposite angles);

CO=OD, (O, the midpoint of CD)

So by SAS postulate we have

△AOC≅△BOD.

Hence, AC = BD, as they are corresponding parts of congruent triangles.

d) Given: AD is the perpendicular bisector of BC means ∠ADB = ∠ADC = 90° and BD = DC

To Prove: ΔABC is an isosceles triangle in which AB = AC.

In ΔADC and ΔADB,

AD = AD (Common)

∠ADC = ∠ADB (Each 90°)

CD = BD (AD is the perpendicular bisector of BC)

∴ ΔADC ≅ ΔADB (By SAS congruence rule)

∴ AB = AC (By CPCT)

Therefore, ABC is an isosceles triangle in which AB = AC.

(draw a figure for more help)

hope it was helpful

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Naisha Sharma

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