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## Example Questions

### Example Question #1 : Calculating If Two Acute / Obtuse Triangles Are Similar

is an equilateral triangle. Points are the midpoints of , respectively. is constructed.

All of the following are true *except*:

**Possible Answers:**

The perimeter of is twice that of .

All of the statements in the other four choices are correct.

Each side of is parallel to a side of .

The area of is twice that of .

**Correct answer:**

The area of is twice that of .

The three sides of are the midsegments of , so is similar to .

By the Triangle Midsegment Theorem, each is parallel to one side of .

By the same theorem, each has length exactly half of that side, giving twice the perimeter of .

But since the sides of have twice the length of those of , the area of , which varies directly as the square of a sidelength, must be four times that of .

The correct choice is the one that asserts that the area of is twice that of .

### Example Question #124 : Triangles

.

Order the angles of from least to greatest measure.

**Possible Answers:**

The angles of cannot be ordered from the information given.

**Correct answer:**

In a triangle, the angle of greatest measure is opposite the side of greatest measure, and the angle of least measure is opposite the side of least measure. , so their opposite angles are ranked in this order - that is, .

Corresponding angles of similar triangles are congruent, so, since , .

Therefore, by substitution, .

### Example Question #2 : Calculating If Two Acute / Obtuse Triangles Are Similar

The triangles are similar. What is the value of x?

**Possible Answers:**

**Correct answer:**

The proportions of corresponding sides of similar triangles must be equal. Therefore, . .

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