Which pair of triangles can be proven congruent by sas?

QuestionsCategory: General MathWhich pair of triangles can be proven congruent by sas?
BPATC asked 1 month ago
Pic 2
Pic 3
Pic 4
1 Answers
BPATC answered 1 month ago

The answer is the first pair. Let me explain why.

The first pair of triangles can be proven congruent by SAS.

SAS means side angle side. If two triangles are to be congruent, they have to follow some rules. The opposite sides of the two triangles will be equal, and the angles they include will be equal. If the opposite sides and angles of a triangle are equal to the opposite sides and angles of another triangle, then the two triangles are congruent.

Two similar triangles may or may not be congruent

From the following pic, we can see four pics of triangles, and each picture contains two triangles. We need to find which triangle is congruent. We already know the rules. Let’s match them with each image.

Pic 1

In this picture, we can see that the two sides of both triangles are congruent. And the angles of both the triangles are equal to 90 degrees. The opposite arm of both triangles and the angle adjacent to the arm are equal. So the triangle of the first figure is congruent.

Here in this figure, both sides of the triangle represent SS

And the angle between the side is corresponding which implies SAS

This means that the first pair of triangles are congruent by SAS postulate

Pic 2

In the second picture, we can see that the two angles of both triangles are congruent. This is similar to the first pictures. Both triangles share a common side. That means this triangle is also congruent. But this doesn’t follow SAS rules. Let’s see why

The two congruent angles represent AA

The common side implies ASA.

This means that the second pair of triangles are congruent by the ASA postulate.

Pic 3 And 4

Both pictures have a similar case. All sides of both triangles are congruent. 

This means that the third and the fourth pairs of triangles are congruent by the SSS postulate.

So the current answer is picture 1.

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