Are the triangles in the drawing congruent?
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Are the triangles in the drawing congruent?
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:
We proceed with the sections accordingly:
We place this value in the right triangle we should find the length of the side:
However since it is not possible for the length of a side to be equal to 0, the triangles are not congruent.
No
Look at the triangles in the diagram.
Which of the statements is true?
In geometry, side lengths represent distances, which must always be positive numbers. A side of length 0 means no side exists, and negative lengths are impossible in real triangles.
Never ignore impossible geometric conditions! Even if your algebra is correct, you must check that your answer makes physical sense in the geometric context.
No! For congruence, we need , which only has one solution: X = -2. Since this gives an impossible side length, the triangles can never be congruent.
S.A.S means Side-Angle-Side: two triangles are congruent if they have two pairs of equal sides with the included angle between those sides also equal.
Choose based on what information is given in the problem.
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