One of the angles of  - namely,  - is marked as a right angle. This makes , by definition, a right triangle.

A congruency statement about two triangles implies nothing about the relationship between two angles of one of the triangles, so  is not correct.

Also, letters in the same position between the two triangles refer to corresponding - and subsequently, congruent - angles. Therefore,  implies that:

Of the given choices, only  is a consequence. It is the correct response.

The triangle has an exterior angle of , so it has an interior angle of . By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles; there are two possible scenarios that fit this criterion:

Case 1: Two angles have measure . The third angle will have measure

.

 will be the greatest of the angle measures.

Case 2: One angle has measure  and the others are congruent. Their common measure will be

.

 will be the greatest of the angle measures.

The given information is therefore inconclusive.

The triangle has an exterior angle of , so it has an interior angle of . By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles; there are two possible scenarios that fit this criterion:

Case 1: Two angles have measure . The third angle will have measure

.

 will be the least of the angle measures.

Case 2: One angle has measure  and the others are congruent. Their common measure will be

.

 will be the least of the angle measures.

In both cases, the least of the degree measures of the angles will be .

The triangle has an exterior angle of , so it has an interior angle of .

Since this is an obtuse angle, its other two angles must be acute. By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles - the acute angles are those. Since the sum of their measures is the same as their remote exterior angle -  - each has measure .This is the correct response.

The triangle has an exterior angle of , so it has an interior angle of .

Since this is an obtuse angle, its other two angles must be acute. Therefore, this angle is the one of greatest measure.

The degree measures of a triangle must total , so we find the sum of the degree measures in each choice.

: 

:

:

:

This is the correct choice.

Since corresponding parts of congruent triangles are congruent, it follows that . Therefore, , by definition, bisects , and the first statement is true. A bisector of an angle of an equilateral triangle is also the perpendicular bisector of the opposite side, so the other two statements are immediate consequences. 

Every equilateral triangle has three congruent angles - all of which have measure  - as a result of the Isosceles Triangle Theorem. Therefore, the statements:

 is an acute triangle

immediately follow.

However, if  and  are complementary, then the sum of their measures is ; since each angle measures , then their measures add up to . This is the correct choice.

By the Isosceles Triangle Theorem, angles opposite congruent sides of a triangle are congruent. Therefore, a scalene triangle, having three noncongrent sides, must have three noncongruent angles.

 can be eliminated immediately.

For the other three choices, we need to find the measure of the third angle using the fact that the degree measures of the angles of a triangle must total .

: 

The third angle measure is .

This triangle has two  angles and can be eliminated.

:

The third angle measure is .

This triangle has two  angles and can be eliminated.

:

The third angle measure is .

This triangle has three angles of different measure, making it scalene. This is the correct choice.