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Which triangles must be congruent? two isosceles triangles, each with both legs 40 inches long. two isosceles triangles, each with a base 40 inches long. two right triangles, each with both legs 40 inches long. two right triangles, each with a hypotenuse 40 inches long.



Answer :

sqdancefan

Answer:

  (c)  two right triangles, each with both legs 40 inches long

Step-by-step explanation:

You want to know which pair of triangles are congruent, given their descriptions.

Congruent triangles

There are basically 4 theorems that allow you to claim congruence of triangles:

  AAS, ASA, SAS, SSS

A fifth one applies to right triangles only: HL.

These tell you that you need to have three matching parts: 3 sides, 2 sides and the angle between (except right triangle), or 1 side and 2 angles.

Choices

An isosceles triangle with only one or two sides defined is not sufficient.

A right triangle with only the hypotenuse defined is not sufficient.

A right triangle with two legs and the (right) angle between them has a sufficient number of matching parts to be able to claim congruence to another triangle similarly defined.

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