Question

is it possible to show that \\( \triangle a b c \\) is congruent to \\( \triangle d b e \\)? explain.

Explanation:

Step1: Identify the given information

From the figure, we have \(BC = BE\) (marked with one tick), \(AB = DB\) (marked with two ticks), and \(\angle ABC=\angle DBE = 90^{\circ}\) (right - angle marks).

Step2: Apply the congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
For \(\triangle ABC\) and \(\triangle DBE\), we have:

• \(AB = DB\) (given)
• \(\angle ABC=\angle DBE\) (both are right angles)
• \(BC = BE\) (given)

Answer:

Yes, \(\triangle ABC\cong\triangle DBE\) by the Side - Angle - Side (SAS) congruence criterion.