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.

One yard is equal to three feet, and one foot is equal to twelve inches. Therefore, 9 feet is equal to  inches, and 3 yards is equal to  inches. The triangle has sides of measure 90 inches, 108 inches, and 108 inches. Exactly two sides are of equal measure, so it is isosceles but not equilateral.

The sum of the three interior angles of a triangle is 180 degrees.

Set up an equation such that all three angles are equal to 180 degrees.

Combine like-terms.

Subtract 34 on both sides.

Divide by 6 on both sides.

The answer is:  

The isosceles triangle has two congruent sides and two congruent angles.  

The interior angles will sum to 180 degrees.

Let the unknown angles be .  These angles are congruent to each other because the triangle is isosceles.

Divide by 2 on both sides.

The answer is:  

 is indicated to be isosceles, with , so, by the isosceles triangle theorem, 

.

Since the measures of the interior angles of a triangle total , 

Substitute  for  and  for , then solve for :

Subtract  from both sides:

Multiply both sides by :

 is an exterior angle of ; its measure is the sum of those of its remote interior angle,  and , so 

Substitute and add:

.

An isosceles has two equivalent base angles.  We can set up an equation such that both angles with the vertex angle add up to 180 degrees.

Solve for , which is a base angle.  Subtract 30 from both sides.

Divide by 2 on both sides.

The answer is:  

Start by figuring out the degree measurements of each angle.

Since we know that the angles of a triangle must add up to , we can write the following equation:

Solve for .

Now, we know the measure of the angles:

Since each angle of the triangle is different, this means the the legs of the triangle must also be different. Thus, this is a scalene triangle.