Step 1: Recall the sum of the angles of a triangle...

The sum of the internal angles of a triangle is .

Step 2: To find the missing angle, subtract the given angles from ...

One yard is equal to 3 feet; it is also equal to 36 inches. Therefore:

18 feet is equal to  yards, 

and

216 feet is equal to  yards.

The three sides are congruent, making the triangle equilateral - and all equilateral triangles are acute.

You can find the length of c by first finding the length of the hypotenuse of the larger similar triangle and then setting up a ratio to find the hypotenuse of the smaller similar triangle. 

You also could have found 10 by recognizing this triangle is a form of a 3-4-5 triangle. 

The hypotenuse of the bigger triangle is 10 inches.

Now that we know the length of the hypotenuse for the larger triangle, we can set up a ratio equation to find the hypotenuse of the smaller triangle. 

cross multiply

Read the question carefully and notice that the image is deceptive: these lines are not parallel. So we cannot apply any of our rules about parallel lines. So we cannot infer II or III, those are only true if the lines are parallel. If we sketch line 2 and line 3 meeting we will form a triangle and it is possible to make a = e. One such solution is to make a and e 60 degrees. 

Try sketching it out.

Start with one circle and then keep adding circles like a venn diagram and start counting. A region is any portion of the figure that can be defined and has a boundary with another portion. Don't forget that the exterior (labeled 14) is a region that does not have exterior boundaries.

Notice that the figure may not be to scale, and points  and  could lie anywhere on line segments  and  respectively.

Next, recall the formula for the area of a triangle:

To find the minimum area we need the smallest possible values for  and .

To make  smaller we can shift points  and  all the way to point . This will make triangle  have a height of :

 is the minimum possible value for the area.

To find the maximum value we need the largest possible values for  and . If we shift point  all the way to point  then the base of the triangle is  and the height is , which we can plug into the formula for the area of a triangle:

which is the maximum possible area of triangle 

One foot is equal to 12 inches, so the triangle would have sides 10, 12, and 24 inches. Since 

,

the triangle violates the Triangle Inequality, which states that the sum of the lengths of the two smaller sides must exceed the length of the third. The triangle cannot exist.

Nine yards is equal to  inches.

30 feet is equal to  inches.

In terms of inches, the triangle has sides of length 324, 360, 360; this exists since

and this is an isosceles triangle, since two sides have the same length.

Also,

,

making the triangle acute.

Collinear points are points that are contained in the same line. Of the four choices, only  fit the description, since all are on Line .

 gives us the congruence of two corresponding angles and one corresponding side;  this is not enough to establish similarity.

The perimeters of the triangles are irrelevant to their similarity, so  and  having the same perimeter does not help to establish similarity, with or without what is given.

 establishes the proportionality of two nonincluded sides of the angles known to be congruent. However, there is no statement that establishes similarity as a result of this.

, along with , sets up the conditions of the Angle-Angle Similarity Postulate, which states that if two triangles have two pairs of congruent angles between them, the triangles are similar.  is the correct choice.