In the figure O is the midpoint of AB and CD. Prove that
(i) $△ A O C ≅ △ B O D$ ; (ii) $A C = B D$ .

Question

In the figure O is the midpoint of AB and CD- Prove that-i- triangle AOC cong triangle BOD- -ii- AC - BD-

Toppr Admin · Accepted Answer

In triangles AOC and BOD- we haveAO - BO -O- the midpoint of AB-x2220-AOC-x2220-BOD- -vertically opposite angles-CO-OD- -O- the midpoint of CD-So by SAS postulate we have-x25B3-AOC-x2245-x25B3-BOD-Hence- AC - BD- as they are corresponding parts of congruent triangles-

In the figure O is the midpoint of AB and CD. Prove that(i) △AOC≅△BOD; (ii) AC=BD.

In triangles AOC and BOD, we haveAO = 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.

In the figure O is the midpoint of AB and CD. Prove that
(i) $△ A O C ≅ △ B O D$ ; (ii) $A C = B D$ .

In triangles AOC and BOD, we have
AO = BO (O, the midpoint of AB);
$∠ A O C = ∠ B O D$ , (vertically opposite angles);
$C O = O D$ , (O, the midpoint of CD)
So by SAS postulate we have
$△ A O C ≅ △ B O D$ .
Hence, AC = BD, as they are corresponding parts of congruent triangles.