Question

Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate?

Answer

Triangle ABD and Triangle ECD
Triangle ABD and Triangle ADC
Triangle ADC and Triangle ABC
Triangle ABC and Triangle ECD

Answer 1

Triangle ABD and Triangle ECD
''''''''''''''''Remember: Vertical angles are congruent '''''''''''''''''''''
So angle ADB and angle CDE are congruent
We know that sides BD and DC are congruent
also sides AD and DE are congruent

:)

Answer 2

Answer: Triangle ABC and Triangle ECD

Explanation:

In Triangle ABC and Triangle ECD

BD=CD and AD=ED [given in the figure]

∠BDA=∠EDC [Vertically opposite angles are equal]

⇒ΔABC ≅ ΔECD [By SAS postulate]

SAS postulate or Side Angle Side postulate tells that if two sides and their included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.