How to find if rectangles are similar - Geometry
Card 0 of 48
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.
Compare your answer with the correct one above
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
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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:
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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:
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
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.
Compare your answer with the correct one above