Question

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

(My guess is C)

A: Triangle ABE and triangle BEC
B: Triangle ABC and triangle EBC
C: Triangle BCE and triangle DCE
D: Triangle ACB and triangle ECD

Answer 1

Hi there!

The side angle side postulate states that two triangles are congruent if 2 sides and an included angle on each triangle are congruent. If you take a look at the diagram, there are quite a few triangles. You have to imagine pulling each set of triangles out and looking at the markings. For this question, the correct answer is D - Triangle ACB and Triangle ECD. This is because if you look at EC and AC, they both have one line on them, meaning that they are congruent. The same goes for CB and CD.

Hope this helps!! :)
If something doesn't make sense about my answer or you need help with another problem, please let me know!

Answer 2

Answer: The correct option is D.

Step-by-step explanation:

Reason for correct option:

From the given figure it is noticed that,

`AC=EC`

According to the vertical angle theorem the two vertical opposite angles are equal.

`\angle ACB=\angle ECD`

`CD=CB`

So by SAS rule of congruent triangles the triangle ACB is congruent to the triangle ECD.

Reason for incorrect option:

The side AB is not equal to BE, so the option A and B are incorrect.

The angle BCE is not equal to the angle DCE, so the option C is incorrect.