# GMAT Math : Calculating if two acute / obtuse triangles are similar

## 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:

The perimeter of is twice that of . Each side of is parallel to a side of .

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

The area of is twice that of .

The area of is twice that of .

Explanation:

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

Order the angles of from least to greatest measure.    The angles of cannot be ordered from the information given. Explanation:

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 #3 : Calculating If Two Acute / Obtuse Triangles Are Similar The triangles are similar. What is the value of x?     The proportions of corresponding sides of similar triangles must be equal. Therefore, . . 