Mathematics, 15.07.2019 09:00 melinalange48

Which pair of triangles can be proven congruent by sas?

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Answer from: bryanmcmillianjr

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

Step-by-step explanation:

SAS postulate says that if two sides and the included angle of a triangle are equal to two sides and the included angle of another triangle, then the two triangles are said to be congruent.

In the first pair of triangles the included angle of a triangle are equal to two sides and the included angle of another triangle, therefore by SAS postulate the two triangles are said to be congruent.

In the second figure, the pair of triangles are congruent by ASA postulate not SAS.

In the third figure, the pair of triangles are not congruent by any postulate or theorem [Because there is no SSA rule].

In the fourth figure, the pair of triangles are congruent by SSS postulate not SAS.

Answer from: jaici68

Similar triangles may or may not be congruent.

The pair of triangles that can be proved by SAS is (a) the first pair

From the attached figures, we have the following observations

Figure 1

Two sides of both triangles are congruentThe angles between the sides are corresponding

The two congruent sides represent SS

The corresponding angles imply: SAS

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

Figure 2

Two angles of both triangles are congruentThe triangle share a common side

The two congruent angles represent AA

The common side imply: ASA

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

Figure 3 and 4

All sides of both triangles are congruent

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

Hence, the pair of triangles that can be proved by SAS is (a) the first pair

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