Determine whether or not the triangle each pair below are congruent. Justify your conclusion.

  a, b, d — congruent

  c — not congruent

Step-by-step explanation:

a) Both right triangles have side lengths of 6, 8, and 10. (In each triangle, two of those numbers are given. The third is found using the Pythagorean theorem, or by simply matching these numbers to the Pythagorean triple (6, 8, 10). Given any two sides of a right triangle, there is no doubt as to the measure of the third one.

The triangles are congruent by SSS. (For SSS, you do have to find the measure of the missing side.)

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b) The triangles are congruent by AAS. Corresponding sides and angles are marked congruent.

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c) The triangles are not congruent. Two sides are congruent, but the marked angles are not corresponding. One triangle has no necessary relationship to the other.

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d) The triangles are congruent by SAS. The marked angle is between a shared side and the marked side. The shared side of the triangles is actually a diagonal of the parallelogram (figure is not to scale).

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.