Question

In the adjoining figure, AC =50 cm, BD=120, O is the midpoint AC and BD and AC perpendicular to BD. Find the length of AB and CD. Are they equal? ​

Answer 1

$a ) \: \frac{}{3}$

$b) \: 5 \times\frac{}{c}$

$c) \: 13 \times \frac{}{c}$

$d) \: 15 \times \frac{}{c}$

Answers → a) is a correct answer

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step by step:

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.