Question

△ABC has interior angles with measures x°, 100°, and 70°, and △DEF has interior angles with measures y°, 70°, and 20°. Using the given information, which statement is true? The triangles are similar because they each have an interior angle with a measure 70°. The two triangles are not similar because x≠y . The two triangles are not similar because y=90 so it is impossible to have three congruent angles. The two triangles are not similar because the interior angles are congruent but the side lengths are different.

Answer 1

The two triangles are not congruent because y=90°, and therefore the angles from each triangle are not congruent to the angles from the other.

Answer 2

△ABC has interior angles with measures x°, 100°, and 70°.

By using angle sum property, which states that the sum of measures of all three angles is 180 degrees.

$x^{\circ}+100^{\circ}+70^{\circ}=180^{\circ}$

$x^{\circ}=10^{\circ}$

Now, △DEF has interior angles with measures y°, 70°, and 20°.

By using angle sum property,

$y^{\circ}+70^{\circ}+20^{\circ}=180^{\circ}$

$y^{\circ}=90^{\circ}$

Now, we can say that,

"The two triangles are not similar because x≠y"

As one angle of measure 70 degree is common in both the triangles.

If 'x' would be equal to 'y' , then we could say that the triangles are similar by AA criteria.

Therefore, the two triangles are not similar because x is not equal to y.