Quadrilaterals - Basic Geometry
Card 0 of 20
Two rectangles are similar. One rectangle has dimensions 
centimeters and 100 centimeters; the other has dimensions 400 centimeters and 
centimeters.
What value of 
makes this a true statement?
Two rectangles are similar. One rectangle has dimensions
What value of
For polygons to be similar, side lengths must be in proportion.
Case 1:
and 100 in the first rectangle correspond to 
and 400 in the second, respectively.
The resulting proportion would be:
This is impossible since 
must be a positive side length.
Case 2:
and 100 in the first rectangle correspond to 400 and 
in the second, respectively.
The correct proportion statement must be:
Cross multiply to solve for 
:
200 cm is the only possible solution.
For polygons to be similar, side lengths must be in proportion.
Case 1:
The resulting proportion would be:
This is impossible since
Case 2:
The correct proportion statement must be:
Cross multiply to solve for
200 cm is the only possible solution.
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Note: figure not drawn to scale.
Examine the above figure.
What is 
?
Note: figure not drawn to scale.
Examine the above figure.
What is
By similarity, we can set up the proportion:
Substitute:
By similarity, we can set up the proportion:
Substitute:
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Which of the following is not a necessary condition for rectangles A and B to be similar?
Which of the following is not a necessary condition for rectangles A and B to be similar?
All sides being equal is a condition for congruency, not similarity. Similarity focuses on the ratio between rectangles and not on the equivalency of all sides. As for the statement regarding the equal angles, all rectangles regardless of similarity or congruency have four 90 degree angles.
All sides being equal is a condition for congruency, not similarity. Similarity focuses on the ratio between rectangles and not on the equivalency of all sides. As for the statement regarding the equal angles, all rectangles regardless of similarity or congruency have four 90 degree angles.
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What value of 
makes the two rectangles similar?
What value of
For two rectangles to be similar, their sides have to be proportional (form equal ratios). The ratio of the two longer sides should equal the ratio of the two shorter sides.
However, the left ratio in our proportion reduces.
We can then solve by cross multiplying.
We then solve by dividing.
For two rectangles to be similar, their sides have to be proportional (form equal ratios). The ratio of the two longer sides should equal the ratio of the two shorter sides.
However, the left ratio in our proportion reduces.
We can then solve by cross multiplying.
We then solve by dividing.
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The following images are not to scale.
In order to make these two rectangles similar, what must the width of rectangle on the right be?
The following images are not to scale.
In order to make these two rectangles similar, what must the width of rectangle on the right be?
For two rectangles to be similar, their sides must be in the same ratio.
This problem can be solved using ratios and cross multiplication.
Let's denote the unknown width of the right rectangle as x.
For two rectangles to be similar, their sides must be in the same ratio.
This problem can be solved using ratios and cross multiplication.
Let's denote the unknown width of the right rectangle as x.
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Two rectangles are similar. One has an area of 
and the other an area of 
. If the first has a base length of 
, what is the height of the second rectangle?
Two rectangles are similar. One has an area of
The goal is to solve for the height of the second rectangle.
Similar rectangles function on proportionality - that is, the ratios of the sides between two rectangles will be the same. In order to determine the height, we will be using this concept of ratios through solving for variables from the area.
First, it's helpful to achieve full dimensions for the first rectangle.
It is given that its base length is 5, and it has an area of 20.
This means the first rectangle has the dimensions 5x4.
Now, we may utilize the concept of ratios for similarity. The side lengths of the first rectangle is 5x4, so the second recatangle must have sides that are proportional to the first's.
We have the information for the first rectangle, so the data may be substituted in.
is the ratio factor that will be used to solve for the height of the second rectangle. This may be substituted into the area formula for the second rectangle.
Therefore, the height of the second rectangle is 10.
The goal is to solve for the height of the second rectangle.
Similar rectangles function on proportionality - that is, the ratios of the sides between two rectangles will be the same. In order to determine the height, we will be using this concept of ratios through solving for variables from the area.
First, it's helpful to achieve full dimensions for the first rectangle.
It is given that its base length is 5, and it has an area of 20.
This means the first rectangle has the dimensions 5x4.
Now, we may utilize the concept of ratios for similarity. The side lengths of the first rectangle is 5x4, so the second recatangle must have sides that are proportional to the first's.
We have the information for the first rectangle, so the data may be substituted in.
Therefore, the height of the second rectangle is 10.
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There are two rectangles. One has a perimeter of 
and the second one has a perimeter of 
. The first rectangle has a height of 
. If the two rectangles are similiar, what is the base of the second rectangle?
There are two rectangles. One has a perimeter of
The goal of this problem is to figure out what base length of the second rectangle will make it similar to the first rectangle.
Similar rectangles function on proportionality - that is, the ratios of the sides between two rectangles will be the same. In order to determine the base, we will be using this concept of ratios through solving for variables from the perimeter.
First, all the dimensions of the first rectangle must be calculated.
This can be accomplished through using the perimeter equation: 
This means the dimensions of the first rectangle are 10x5. We will use this information for the ratios to calculate dimensions that would yield the second rectangle similar because of proprotions.
is the ratio factor we will use to solve for the base of the second rectangle.
This will require revisiting the perimeter equation for the second rectangle.
The goal of this problem is to figure out what base length of the second rectangle will make it similar to the first rectangle.
Similar rectangles function on proportionality - that is, the ratios of the sides between two rectangles will be the same. In order to determine the base, we will be using this concept of ratios through solving for variables from the perimeter.
First, all the dimensions of the first rectangle must be calculated.
This can be accomplished through using the perimeter equation:
This means the dimensions of the first rectangle are 10x5. We will use this information for the ratios to calculate dimensions that would yield the second rectangle similar because of proprotions.
This will require revisiting the perimeter equation for the second rectangle.
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The attached image represents the dimensions of two different brands of manufactured linoleum tile. If the two tiles are similar, what would be the length of the large tile, given the information in the figure below?
The attached image represents the dimensions of two different brands of manufactured linoleum tile. If the two tiles are similar, what would be the length of the large tile, given the information in the figure below?
Two rectangles are similar if their length and width form the same ratio. The small tile has a width of 
and a width of 
, providing us with the following ratio:
Since the length of similar triangles is twice their respective width, the length of the large tile can be determined as such:
Two rectangles are similar if their length and width form the same ratio. The small tile has a width of
Since the length of similar triangles is twice their respective width, the length of the large tile can be determined as such:
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Are these rectangles similar?
Are these rectangles similar?
To determine if these rectangles are similar, set up a proportion:
This proportion compares the ratio between the long sides in each rectangle to the ratio of the short sides in each rectangle. If they are the same, cross-multiplying will produce a true statement, and the rectangles are similar:
These rectangles aren't similar.
To determine if these rectangles are similar, set up a proportion:
These rectangles aren't similar.
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Are these rectangles similar?
Are these rectangles similar?
To determine if the rectangles are similar, set up a proportion comparing the short sides and the long sides from each rectangle:
cross-multiply
since that's true, the rectangles are similar.
To find the scale factor, either divide 25 by 10 or 7.5 by 3. Either way you will get 2.5.
To determine if the rectangles are similar, set up a proportion comparing the short sides and the long sides from each rectangle:
To find the scale factor, either divide 25 by 10 or 7.5 by 3. Either way you will get 2.5.
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Figure NOT drawn to scale
Refer to the above figure.
True or false: Rectangle 
Rectangle 
.
Figure NOT drawn to scale
Refer to the above figure.
True or false: Rectangle
Two rectangles are similar if and only if their sides are in proportion. Specifically,
Rectangle Rectangle
if
Since 
is located at the point 
, it follows that 
and 
. Since 
is located at the point 
, it follows that 
and 
. Substituting in the aforementioned proportion statement, we get
.
Reducing to lowest terms, this is
.
This is false, so Rectangle 
Rectangle .
Two rectangles are similar if and only if their sides are in proportion. Specifically,
Rectangle
if
Since
Reducing to lowest terms, this is
This is false, so Rectangle
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Consider the similar rectangles 
and 
shown here. The lengths of the following sides are given:
What is the length of the side 
?
Consider the similar rectangles
What is the length of the side
Comparing the sides 
and 
, we see that
is 
the length of 
, as shown here:
.
Since these two rectangles are similar, all pairs of corresponding sides are similar. Hence, the ratio of 
to 
is also 
, and we can calculate the length of 
by setting up and solving a proportion:
.
Hence, the length of the side 
is 
units.
Comparing the sides
Since these two rectangles are similar, all pairs of corresponding sides are similar. Hence, the ratio of
Hence, the length of the side
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What is the area of the rectangle in the diagram?
What is the area of the rectangle in the diagram?
The area of a rectangle is found by multiplying the length by the width.
The length is 12 cm and the width is 7 cm.
Therefore the area is 84 cm2.
The area of a rectangle is found by multiplying the length by the width.
The length is 12 cm and the width is 7 cm.
Therefore the area is 84 cm2.
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A rectangle has a perimeter of 
. The length is ten meters more than the width. What is the area of the rectangle?
A rectangle has a perimeter of
Given a rectangle, the general equation for the perimeter is 
and area is 
where 
is the length and 
is the width.
Let 
= width and 
= length
So the equation to solve becomes 
so 
thus the width is 
and the length is 
.
Thus the area is 
Given a rectangle, the general equation for the perimeter is
Let
So the equation to solve becomes
Thus the area is
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Which of the following information would not be sufficient to find the area of a rectangle?
Which of the following information would not be sufficient to find the area of a rectangle?
The area of a rectangle can be calculated by multiplying the lengths of two adjacent sides. All of the choices given lists sufficient information, with one exception. We examine each of the choices.
The lengths of one pair of adjacent sides: This choice is false, as is directly stated above.
The perimeter and the length of one side: Using the perimeter formula, you can find the length of an adjacent side, making this choice false.
The lengths of one side and a diagonal: using the Pythagorean Theorem, you can find the length of an adjacent side, making this choice false.
The lengths of one pair of opposite sides: this gives you no way of knowing the lengths of the adjacent sides. This is the correct choice.
The area of a rectangle can be calculated by multiplying the lengths of two adjacent sides. All of the choices given lists sufficient information, with one exception. We examine each of the choices.
The lengths of one pair of adjacent sides: This choice is false, as is directly stated above.
The perimeter and the length of one side: Using the perimeter formula, you can find the length of an adjacent side, making this choice false.
The lengths of one side and a diagonal: using the Pythagorean Theorem, you can find the length of an adjacent side, making this choice false.
The lengths of one pair of opposite sides: this gives you no way of knowing the lengths of the adjacent sides. This is the correct choice.
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Find the area of the polygon.
Find the area of the polygon.
Drawing a vertical line at the end of the side of length 
divides the shape into a rectangle and a right triangle.
The sum of the areas of the two shapes is the area of the polygon. Multiply the length of the rectangle by its width to find the area of the rectangle, and use the formula 
, where 
is the base and 
is the height of the triangle, to find the area of the triangle. Adding them together gives the answer.
Drawing a vertical line at the end of the side of length
The sum of the areas of the two shapes is the area of the polygon. Multiply the length of the rectangle by its width to find the area of the rectangle, and use the formula
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One side of a rectangle is 7 inches and another is 9 inches. What is the area of the rectangle in inches?
One side of a rectangle is 7 inches and another is 9 inches. What is the area of the rectangle in inches?
To find the area of a rectangle, multiply its width by its height. If we know two sides of the rectangle that are different lengths, then we have both the height and the width.
To find the area of a rectangle, multiply its width by its height. If we know two sides of the rectangle that are different lengths, then we have both the height and the width.
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What is the area of a rectangle whose length and width is 
inches and 
inches, respectively?
What is the area of a rectangle whose length and width is
The area of any rectangle with length, 
and width, 
is:
The area of any rectangle with length,
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What is the area of a rectangle that has a length of 
and a width of 
?
What is the area of a rectangle that has a length of
Recall how to find the area of a rectangle:
Now, plug in the given length and width to find the area.
Recall how to find the area of a rectangle:
Now, plug in the given length and width to find the area.
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What is the area of a rectangle that has a length of 
and a width of 
?
What is the area of a rectangle that has a length of
Recall how to find the area of a rectangle:
Now, plug in the given length and width to find the area.
Recall how to find the area of a rectangle:
Now, plug in the given length and width to find the area.
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