GED Math : Angles and Quadrilaterals
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Example Questions
Example Question #1 : Angles And Quadrilaterals
In Rhombus 
The figure referenced is below.
The sides of a rhombus are congruent by definition, so 
Also, consecutive angles of a rhombus are supplementary, as they are with all parallelograms, so
The correct response is that 
Example Question #2 : Angles And Quadrilaterals
Given Quadrilateral 
I) 
II) 
III) 
Statement I, II, or III
Statement II only
Statement I only
Statement III only
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 #3 : Angles And Quadrilaterals
You are given Parallelogram 
I)
II)
III)
Statement I only
Statement III only
Statement II only
Statement I, II, or III
Statement I, II, or III
A rectangle is defined as a parallelogram with four right, or 
Since opposite angles of a paralellogram are congruent, if one angle measures 
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 #1 : Angles And Quadrilaterals
If the rectangle has a width of 5 and a length of 10, what is the area of the rectangle?
Write the area for a rectangle.
Substitute the given dimensions.
The answer is:
Example Question #1 : Angles And Quadrilaterals
In the figure below, find the measure of the largest angle.
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 
The largest angle is 
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