Similar Figure

Front

What is the definition of similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

How do you set up a proportion to find the height of an object using shadows?

Back

To set up a proportion, use the ratio of the height of the object to the length of its shadow, and set it equal to the ratio of the height of the other object to the length of its shadow.

Front

If a tree is 12 feet tall and casts a shadow of 9 feet, what is the height of a building that casts a shadow of 24 feet?

Back

The height of the building is 32 feet, calculated using the proportion: 12/9 = x/24.

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

What does it mean for angles in similar figures to be congruent?

Back

It means that all corresponding angles in similar figures have the same measure.

Front

How do you find the coordinates of a point after dilation?

Back

To find the coordinates of a point after dilation, multiply the distance from the center of dilation to the point by the scale factor and then add the coordinates of the center of dilation.

Front

What is the relationship between the sides of similar figures?

Back

The corresponding sides of similar figures are proportional, meaning the ratios of their lengths are equal.

Front

What is the formula for finding the missing length in a proportion?

Back

If you have a proportion a/b = c/d, you can find the missing length by cross-multiplying: a*d = b*c.

Front

In the proportion CB / DM = AC / ?, what does AD represent?

Back

AD represents the missing length that corresponds to AC in the proportion.

Front

What is the significance of the center of dilation in a geometric transformation?

Back

The center of dilation is the fixed point in the plane about which all points are expanded or contracted during the dilation.