Angles and Quadrilaterals - GED Math
Card 0 of 5
In Rhombus 
, 
. If 
is constructed, which of the following is true about 
?
In Rhombus
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.
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
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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
Given Quadrilateral
I)
II)
III)
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.
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.
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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) 
You are given Parallelogram
I)
II)
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.
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.
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If the rectangle has a width of 5 and a length of 10, what is the area of the rectangle?
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: 
Write the area for a rectangle.
Substitute the given dimensions.
The answer is:
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In the figure below, find the measure of the largest angle.
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 
into each expression for each angle.
The largest angle is 
.
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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