Plane Geometry - SSAT Middle Level Math
Card 0 of 20
Figure NOT drawn to scale.
Evaluate 
.
Figure NOT drawn to scale.
Evaluate
By the Segment Addition Postulate,
By the Segment Addition Postulate,
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Figure NOT drawn to scale.
Evaluate 
.
Figure NOT drawn to scale.
Evaluate
By the Segment Addition Postulate,
By the Segment Addition Postulate,
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What is the length of a line segment with end points 
and 
?
What is the length of a line segment with end points
The length of a line segment can be determined using the distance formula:
The length of a line segment can be determined using the distance formula:
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What is the length of a line with endpoints 
and 
.
What is the length of a line with endpoints
To find the length of this line, you can subtract 
to get 
. Since the y-coordinates are the same, you don't have to take any vertical direction into account. Therefore, you only look at the x-coordinates!
To find the length of this line, you can subtract
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Find the length of the line segment whose endpoints are 
and 
.
Find the length of the line segment whose endpoints are
We can use the distance formula:
We can use the distance formula:
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The point 
lies on a circle. What is the length of the radius of the circle if the center is located at 
?
The point
The radius is the distance from the center of the circle to anypoint on the circle. So we can use the distance formula in order to find the radius of the circle:
The radius is the distance from the center of the circle to anypoint on the circle. So we can use the distance formula in order to find the radius of the circle:
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The coordinates of 
and 
are 
and 
. Find the length of the diagonal of the following rectangle:
The coordinates of
A rectangle has two diagonals with the same length. So we should find the length of 
. We can use the distance formula:
A rectangle has two diagonals with the same length. So we should find the length of
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The radius of a circle is 6 inches. What is one-third of the diameter?
The radius of a circle is 6 inches. What is one-third of the diameter?
If the radius is equal to 6 inches, then the diameter will be double that value, or 12 inches. One-third of 12 is 4, which is therefore the correct answer.
If the radius is equal to 6 inches, then the diameter will be double that value, or 12 inches. One-third of 12 is 4, which is therefore the correct answer.
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If a circle has a radius of 12 inches, the biggest line that would be drawn within the circle is:
If a circle has a radius of 12 inches, the biggest line that would be drawn within the circle is:
The largest line that can be drawn within a circle is the diamater. The diameter is equal to twice the radius. Given that the radius is equal to 12 inches, the largest line that could be drawn (the diameter) would be equal to 24 inches.
The largest line that can be drawn within a circle is the diamater. The diameter is equal to twice the radius. Given that the radius is equal to 12 inches, the largest line that could be drawn (the diameter) would be equal to 24 inches.
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A right triangle has one leg with a length of 6 feet and a hypotenuse of 10 feet. What is the length of the other leg?
A right triangle has one leg with a length of 6 feet and a hypotenuse of 10 feet. What is the length of the other leg?
In geometry, a right angle triangle can occur with the ratio of 
in which 3 and 4 are each leg lengths, and 5 is the hypotenuse.
When you know the length of two sides of a right angle triangle like this, you can calculate the third side using this ratio.
Here, the ratio is:
This is double the 
ratio. Therefore, we should multiply 4 by 2 in order to solve for the missing leg, which would be a value of 8 feet.
Another way to solve is to use the Pythagorean Theorem: 
.
We know that one leg is 6 feet and the hypotenuse is 10 feet.
In geometry, a right angle triangle can occur with the ratio of
When you know the length of two sides of a right angle triangle like this, you can calculate the third side using this ratio.
Here, the ratio is:
This is double the
Another way to solve is to use the Pythagorean Theorem:
We know that one leg is 6 feet and the hypotenuse is 10 feet.
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The diameter of a circle is 
centimeters. What is one-fourth of the circle's radius?
The diameter of a circle is
By definition, the radius 
and diameter 
of a circle are related by the following equation:
Plugging in 
as stated in the question, we find that 
.
Since the question is asking us for the value of 
:
.
By definition, the radius
Plugging in
Since the question is asking us for the value of
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A right triangle has one leg with length 
and another leg with length 
. What is the length of the hypotenuse?
A right triangle has one leg with length
Since we are dealing with a right triangle, we can use the Pythagorean Theorem:
,
where 
and 
are leg lengths of 
and 
, respectively, and 
is the length of the hypotenuse.
Substituting values into the Theorem:
Since we are dealing with a right triangle, we can use the Pythagorean Theorem:
where
Substituting values into the Theorem:
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Line 
has a length of 
. It is bisected at point 
, and the resulting segment 
is bisected again at point 
. What is the length of the line segment 
?
Line
A line that is bisected is split into two segments of equal length. Therefore, if line 
is bisected at point 
,
.
Consequently, bisecting line segment 
at point 
:
A line that is bisected is split into two segments of equal length. Therefore, if line
Consequently, bisecting line segment
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A triangle has sides 
feet, 
feet, and 
feet. Calculate its perimeter.
A triangle has sides
The perimeter of any figure is the sum of the lengths of the sides: 
.
The perimeter of any figure is the sum of the lengths of the sides:
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Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?
Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?
An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.
This makes the perimeter either
or
Of our choices, we choose 38.
An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.
This makes the perimeter either
or
Of our choices, we choose 38.
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The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?
The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?
Since it is isosceles, 2 of the sides must be equal. They must also add to 18.
Since it is isosceles, 2 of the sides must be equal. They must also add to 18.
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An equilateral triangle has perimeter 
centimeters. How long is one side?
An equilateral triangle has perimeter
An equilateral triangle has three sides of equal measure, so divide its perimeter by 
:
An equilateral triangle has three sides of equal measure, so divide its perimeter by
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An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?
An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?
One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to 
inches.
An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:
To convert 34 inches to feet and inches:
One side measures 2 feet 10 inches.
One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to
An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:
To convert 34 inches to feet and inches:
One side measures 2 feet 10 inches.
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A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?
A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?
By the Pythagorean Theorem, if 
and 
are the legs of a right triangle and 
is its hypotenuse, then
.
Set 
and solve for 
:
The perimeter of the triangle - the sum of the sidelengths - is
.
By the Pythagorean Theorem, if
Set
The perimeter of the triangle - the sum of the sidelengths - is
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Find the perimeter of the triangle above.
Note: Figure not drawn to scale.
Find the perimeter of the triangle above.
Note: Figure not drawn to scale.
The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: 
.
Because the lengths are in inches, the answer must be in inches as well.
The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides:
Because the lengths are in inches, the answer must be in inches as well.
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