### All GED Math Resources

## Example Questions

### Example Question #1 : Angles And Quadrilaterals

In Rhombus , . If is constructed, which of the following is true about ?

**Possible Answers:**

is right and isosceles, but not equilateral

is acute and equilateral

is obtuse and isosceles, but not equilateral

is acute and isosceles, but not equilateral

**Correct answer:**

is obtuse and isosceles, but not equilateral

The figure referenced is below.

The sides of a rhombus are congruent by definition, so , making isosceles (and possibly equilateral).

Also, consecutive angles of a rhombus are supplementary, as they are with all parallelograms, so

.

, having measure greater than , is obtuse, making an obtuse triangle. Also, the triangle is not equilateral, since such a triangle must have three angles.

The correct response is that is obtuse and isosceles, but not equilateral.

### Example Question #1 : Angles And Quadrilaterals

Given Quadrilateral , which of these statements would prove that it is a parallelogram?

I) and

II) and

III) and are supplementary and and are supplementary

**Possible Answers:**

Statement II only

Statement I, II, or III

Statement I only

Statement III only

**Correct answer:**

Statement II only

Statement I asserts that two pairs of consecutive angles are congruent. This does not prove that the figure is a parallelogram. For example, an isosceles trapezoid has two pairs of congruent base angles, which are consecutive.

Statement II asserts that both pairs of opposite angles are congruent. By a theorem of geometry, this proves the quadrilateral to be a parallelogram.

Statement III asserts that two pairs of consecutive angles are supplementary. While all parallelograms have this characteristic, trapezoids do as well, so this does not prove the figure a parallelogram.

The correct response is Statement II only.

### Example Question #1 : Angles And Quadrilaterals

You are given Parallelogram with . Which of the following statements, along with what you are given, would be enough to prove that Parallelogram is a rectangle?

I)

II)

III)

**Possible Answers:**

Statement III only

Statement I, II, or III

Statement II only

Statement I only

**Correct answer:**

Statement I, II, or III

A rectangle is defined as a parallelogram with four right, or , angles.

Since opposite angles of a paralellogram are congruent, if one angle measures , so does its opposite. Since consecutive angles of a paralellogram are supplementary - that is, their degree measures total - if one angle measures , then both of the neighboring angles measure .

In short, in a parallelogram, if one angle is right, all are right and the parallelogram is a rectangle. All three statements assert that one angle is right, so from any one, it follows that the figure is a rectangle. The correct response is Statements I, II, or III.

Note that the sidelengths are irrelevant.

### Example Question #4 : Angles And Quadrilaterals

If the rectangle has a width of 5 and a length of 10, what is the area of the rectangle?

**Possible Answers:**

**Correct answer:**

Write the area for a rectangle.

Substitute the given dimensions.

The answer is:

### Example Question #2 : Angles And Quadrilaterals

In the figure below, find the measure of the largest angle.

**Possible Answers:**

**Correct answer:**

Recall that in a quadrilateral, the interior angles must add up to .

Thus, we can solve for :

Now, to find the largest angle, plug in the value of into each expression for each angle.

The largest angle is .

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