2-Dimensional Geometry - GED Math
Card 1 of 2760
What is the diameter of a circle with a radius of 9?
What is the diameter of a circle with a radius of 9?
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The diameter of a circle is twice the radius:
Plug in the radius value:
The diameter of a circle is twice the radius:
Plug in the radius value:
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What is the radius of a circle given the diameter is 22?
What is the radius of a circle given the diameter is 22?
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The radius is half of the diameter, or 11.
The radius is half of the diameter, or 11.
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An exterior angle of an isosceles triangle measures 
. What is the greatest measure of any of the three angles of the triangle?
An exterior angle of an isosceles triangle measures
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The triangle has an exterior angle of 
, so it has an interior angle of 
.
Since this is an obtuse angle, its other two angles must be acute. Therefore, this angle is the one of greatest measure.
The triangle has an exterior angle of
Since this is an obtuse angle, its other two angles must be acute. Therefore, this angle is the one of greatest measure.
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An exterior angle of an isosceles triangle measures 
. What is the greatest measure of any of the three angles of the triangle?
An exterior angle of an isosceles triangle measures
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The triangle has an exterior angle of 
, so it has an interior angle of 
. By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles; there are two possible scenarios that fit this criterion:
Case 1: Two angles have measure 
. The third angle will have measure
.
will be the greatest of the angle measures.
Case 2: One angle has measure 
and the others are congruent. Their common measure will be
.
will be the greatest of the angle measures.
The given information is therefore inconclusive.
The triangle has an exterior angle of
Case 1: Two angles have measure
Case 2: One angle has measure
The given information is therefore inconclusive.
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An exterior angle of an isosceles triangle measures 
. What is the least measure of any of the three angles of the triangle?
An exterior angle of an isosceles triangle measures
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The triangle has an exterior angle of 
, so it has an interior angle of 
. By the Isosceles Triangle Theorem, an isosceles triangle must have two congruent angles; there are two possible scenarios that fit this criterion:
Case 1: Two angles have measure 
. The third angle will have measure
.
will be the least of the angle measures.
Case 2: One angle has measure 
and the others are congruent. Their common measure will be
.
will be the least of the angle measures.
In both cases, the least of the degree measures of the angles will be 
.
The triangle has an exterior angle of
Case 1: Two angles have measure
Case 2: One angle has measure
In both cases, the least of the degree measures of the angles will be
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Which of the following could give the measures of the three angles of a triangle?
Which of the following could give the measures of the three angles of a triangle?
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The degree measures of a triangle must total 
, so we find the sum of the degree measures in each choice.
:
:
:
:
This is the correct choice.
The degree measures of a triangle must total
This is the correct choice.
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What angle is complementary to 10 degrees?
What angle is complementary to 10 degrees?
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Complementary angles must add up to ninety.
Subtract the given angle from 90 to find the other angle.
The answer is: 
Complementary angles must add up to ninety.
Subtract the given angle from 90 to find the other angle.
The answer is:
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Complementary angles add up to how many degrees?
Complementary angles add up to how many degrees?
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Two angles are complementary when they add up to 
.
Two angles are complementary when they add up to
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Which of the following cannot be true of equilateral triangle 
?
Which of the following cannot be true of equilateral triangle
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Every equilateral triangle has three congruent angles - all of which have measure 
- as a result of the Isosceles Triangle Theorem. Therefore, the statements:
is an acute triangle
immediately follow.
However, if 
and 
are complementary, then the sum of their measures is 
; since each angle measures 
, then their measures add up to 
. This is the correct choice.
Every equilateral triangle has three congruent angles - all of which have measure
immediately follow.
However, if
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Which of the following could be the measures of two angles of a scalene triangle?
Which of the following could be the measures of two angles of a scalene triangle?
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By the Isosceles Triangle Theorem, angles opposite congruent sides of a triangle are congruent. Therefore, a scalene triangle, having three noncongrent sides, must have three noncongruent angles.
can be eliminated immediately.
For the other three choices, we need to find the measure of the third angle using the fact that the degree measures of the angles of a triangle must total 
.
:
The third angle measure is 
.
This triangle has two 
angles and can be eliminated.
:
The third angle measure is 
.
This triangle has two 
angles and can be eliminated.
:
The third angle measure is 
.
This triangle has three angles of different measure, making it scalene. This is the correct choice.
By the Isosceles Triangle Theorem, angles opposite congruent sides of a triangle are congruent. Therefore, a scalene triangle, having three noncongrent sides, must have three noncongruent angles.
For the other three choices, we need to find the measure of the third angle using the fact that the degree measures of the angles of a triangle must total
The third angle measure is
This triangle has two
The third angle measure is
This triangle has two
The third angle measure is
This triangle has three angles of different measure, making it scalene. This is the correct choice.
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For a triangle, suppose a given interior angle is 
degrees and the other two angles are 
. What is the value of 
?
For a triangle, suppose a given interior angle is
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The sum of the three interior angles of a triangle is 180 degrees.
Set up an equation such that all three angles are equal to 180 degrees.
Combine like-terms.
Subtract 34 on both sides.
Divide by 6 on both sides.
The answer is: 
The sum of the three interior angles of a triangle is 180 degrees.
Set up an equation such that all three angles are equal to 180 degrees.
Combine like-terms.
Subtract 34 on both sides.
Divide by 6 on both sides.
The answer is:
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Give the area of the above circle.
Give the area of the above circle.
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The area 
of a circle, given its radius 
, can be found using the formula
The radius is half the diameter - that is, 
- so, substituting,
or
The diameter of the given circle is 7, so set 
in the above formula:
,
the correct area.
The area
The radius is half the diameter - that is,
or
The diameter of the given circle is 7, so set
the correct area.
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Let 
.
Find the area of a circle with a diameter of 12in.
Let
Find the area of a circle with a diameter of 12in.
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To find the area of a circle, we will use the following formula:
where r is the radius of the circle.
Now, we know 
. We also know the diameter is 12in. We know the diameter is two times the radius, so the radius is 6in. Now, we can substitute. We get
To find the area of a circle, we will use the following formula:
where r is the radius of the circle.
Now, we know
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Give the circumference of the above circle. Assume each mark on each axis represents one unit.
Give the circumference of the above circle. Assume each mark on each axis represents one unit.
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The diameter of the circle - the distance from one point to the opposite point - is 10 units, so the circumference is this multiplied by 
, or 
.
The diameter of the circle - the distance from one point to the opposite point - is 10 units, so the circumference is this multiplied by
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What is the area of a circle with a diameter of 
?
What is the area of a circle with a diameter of
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Be careful on several counts for this question. First, remember that you need the radius for calculating area. Therefore, since you know that the diameter is 
, you can say that the radius is 
.
Next, be very careful given that there is already a 
in your radius. The formula for the area of a circle is:
For your data, this is:
Be careful on several counts for this question. First, remember that you need the radius for calculating area. Therefore, since you know that the diameter is
Next, be very careful given that there is already a
For your data, this is:
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Which of the following angles forms a complementary angle pair with 
?
Given that 
Which of the following angles forms a complementary angle pair with
Given that
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Which of the following angles forms a complementary angle pair with 
?
Given that 
Complementary angles sum up to 90 degrees. Therefore, to find our answer, we simply need to do the following:
So, our answer is 33 degrees
Which of the following angles forms a complementary angle pair with
Given that
Complementary angles sum up to 90 degrees. Therefore, to find our answer, we simply need to do the following:
So, our answer is 33 degrees
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Find the the measure of angle B if it is complement of angle A:
Find the the measure of angle B if it is complement of angle A:
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If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:
This gives us a final answer of 15 degrees for angle B.
If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:
This gives us a final answer of 15 degrees for angle B.
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Refer to the above diagram. 
is equilateral; 
. How many of the following statements must be true?
I) 
bisects 
II) 
bisects 
III) 
Refer to the above diagram.
I)
II)
III)
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Since corresponding parts of congruent triangles are congruent, it follows that 
. Therefore, 
, by definition, bisects 
, and the first statement is true. A bisector of an angle of an equilateral triangle is also the perpendicular bisector of the opposite side, so the other two statements are immediate consequences.
Since corresponding parts of congruent triangles are congruent, it follows that
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Find the the measure of angle B if it is complement of angle A:
Find the the measure of angle B if it is complement of angle A:
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If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:
This gives us a final answer of 63 degrees for angle B.
If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:
This gives us a final answer of 63 degrees for angle B.
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Find the the measure of angle B if it is complement of angle A:
Find the the measure of angle B if it is complement of angle A:
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If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:
This gives us a final answer of 42 degrees for angle B.
If two angles are complementary, that means the sum of their degrees of measure will add up to 90. In order to find the measure of angle B, subtract angle A from 90 like shown:
This gives us a final answer of 42 degrees for angle B.
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