Question

By applying SAS congruence condition, state which of the following pairs (Fig. 28) of triangles are congruent. State the result in symbolic form

Answer 1

1) We have OA = OC and OB = OD and$$∠AOB =∠COD which are vertically opposite angles.
Therefore by SAS condition, △AOC ≅ △BOD.

2) We have BD = DC
$$∠ADB =∠ADC = 90°
and AD = AD
Therefore by SAS condition, △ADB ≅ △ADC.

3) We have AB = DC
$\angle$ABD = ∠CDB and BD = DB
Therefore by SAS condition, △ABD ≅ △CBD.

4) We have BC = QR
$$∠ABC =∠PQR = 90°
and AB = PQ
Therefore by SAS condition, △ABC ≅ △PQR.