What information is necessary to prove two triangles are similar by the sas similarity theorem?

SAS similarity theorem says that the two sides of one triangle are proportional to the other sides of the another triangle an one included corresponding angles are congruent.

Further explanation:

SAS similarity theorem says that the two sides of one triangle are proportional to the other sides of the another triangle an one included corresponding angles are congruent.

It can be better explained through an example.

Step 1:

Consider the two triangles that the corresponding sides are written below.

Step 2:

The length of is 8 units and the length of is 32 units.

Therefore, the ratio of and can be expressed as,

Step 3:

The length of is 15 units and the length of is 60 units.

Therefore, the ratio of and can be expressed as,

Step 4:

In the triangle the angle .and in the angle .

These two angles and are corresponding congruent angles.

Step 5:

It can be seen that the ratio of corresponding sides of the triangle are proportionalas,

Therefore, it satisfies the condition of SAS similarity theorem.

Thus, are similar by SAS theorem.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Triangle similarity.

Keywords: Triangle, similarity, sides, proportional, ratio, length, theorem, diagram, corresponding sides, angles, sum, fraction

step-by-step explanation:

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