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Bond [772]
3 years ago
13

Mikhail draws triangles ABC and FED, as shown below, and claims that the two triangles are similar but not congruent.

Mathematics
1 answer:
stiv31 [10]3 years ago
4 0

Answer:

First definitions:

Two triangles are congruent if the corresponding sides are all the same length (one triangle can be a rotation, translation or reflection of the other)

Two triangles are similar if the corresponding interior angles are equal and the corresponding sides are proportional. (so one triangle can be a rotation, translation, reflection or contraction/dilation of the other)

You can notice that two congruent triangles are similar, but two similar triangles are not necessarily congruent.

Then two methods to show that the triangles are similar but not congruent are:

1) show that a sequence of rotations, reflections, translations, and dilations carries triangle ABC onto triangle FED

If we have a dilation, then the sidelengths of the corresponding sides can not be equal, wich implies that the triangles are not congruent.

2) show that 2C 2D and that all corresponding sides are proportional

If the sides are proportional, then it is similar, but not congruent.

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