Question

Which measurements could create more than one triangle?

2 of 4 QUESTION
A triangle with sides measuring 10 cm and 20 cm and an included angle
measuring 65°
A triangle with sides measuring 15 inches, 20 inches, and 25 inches
O A triangle with sides measuring 20 cm, 9 cm, and 10 cm
O A right triangle with acute angles measuring 45° and 45°

Answer 1

Answer: A right triangle with acute angles measuring 45° and 45°

Explanation:

This question is related to the criteria of congruence for triangles.

The criteria are:

SSS (you know the 3 sides)

SAS (you know two sides, and the angle between those two sides)

ASA (you know two angles, and the side between those two angles)

AAS (you know two angles, and one side).

So for the given examples, the only one that does not reach any of those criteria is the last option, where we only have the angles:

45°, 45° and 90°.

This means that we can craft multiple triangles with this data:

this is a triangle rectangle where the length of the cathetus is the same, that is the only restriction.

For example we can have lengths:

1, 1 and √2

or 2, 2 and √(2^2 + 2^2) = √8