Side, Side, Angle Congruence Rule: Ascertaining whether or not the triangles are congruent

Examples with solutions for Side, Side, Angle Congruence Rule: Ascertaining whether or not the triangles are congruent

Exercise #1

Are the triangles in the image congruent?

If so, according to which theorem?

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Step-by-Step Solution

Although the lengths of the sides are equal in both triangles, we observe that in the right triangle the angle is adjacent to the side whose length is 7, while in the triangle on the left side the angle is adjacent to the side whose length is 5.

Since it's not the same angle, the angles between the triangles do not match and therefore the triangles are not congruent.

Answer

No.

Exercise #2

Which of the triangles are congruent?

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Step-by-Step Solution

Let's observe the angle in each of the triangles and note that each time it is opposite to the length of a different side.

Therefore, none of the triangles are congruent since it is impossible to know from the data.

Answer

It is not possible to know based on the data.

Exercise #3

Are the triangles in the drawing congruent?

303030303030X+2X+2X+23333332X+4

Step-by-Step Solution

In order for triangles to be congruent, one must demonstrate that the S.A.S theorem is satisfied

We have a common side whose length in both triangles is equal to 3.

Now let's examine the lengths of the other sides:

2X+4=X+2 2X+4=X+2

We proceed with the sections accordingly:24=2XX 2-4=2X-X

2=X -2=X

We place this value in the right triangle we should find the length of the side:2+2=0 -2+2=0

However since it is not possible for the length of a side to be equal to 0, the triangles are not congruent.

Answer

No