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

Study concepts, example questions & explanations for GMAT Math

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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:

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

The perimeter of  is twice that of .

The area of  is twice that of .

Each side of  is parallel to a side of .

Correct answer:

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

.

Order the angles of  from least to greatest measure.

Possible Answers:

The angles of  cannot be ordered from the information given.

Correct answer:

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

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

Possible Answers:

Correct answer:

Explanation:

The proportions of corresponding sides of similar triangles must be equal. Therefore, \small \frac{8}{12}\ =\ \frac{10}{x}. \small 8x\ =\ 120; x\ =\ 15.

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