GED Math : Angles and Quadrilaterals

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #1 : Angles And Quadrilaterals

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

Possible Answers:

 is acute and equilateral

 is acute and isosceles, but not equilateral

 is obtuse and isosceles, but not equilateral

 is right and isosceles, but not equilateral

Correct answer:

 is obtuse and isosceles, but not equilateral

Explanation:

The figure referenced is below.

Rhombus

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 #2 : 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 only

Statement III only

Statement I, II, or III

Correct answer:

Statement II only

Explanation:

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 only

Statement I, II, or III

Statement II only

Correct answer:

Statement I, II, or III

Explanation:

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:

Explanation:

Write the area for a rectangle.

Substitute the given dimensions.

The answer is:  

Example Question #5 : Angles And Quadrilaterals

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

3

Possible Answers:

Correct answer:

Explanation:

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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