transformations and similarity unit test
1) What is the definition of a transformation in mathematics?
A transformation is a mathematical operation that changes the position, orientation, or size of a shape or image.
2) Identify the type of transformation shown in each example below:
a) A shape is reflected across a line of symmetry. - Reflection
b) A shape is rotated 90 degrees counterclockwise. - Rotation
c) A shape is translated 5 units to the right and 3 units up. - Translation
d) A shape is dilated, making it larger or smaller. - Dilation
3) What is the definition of similarity in mathematics?
Similarity is a property of two shapes in which they have the same shape, but not necessarily the same size.
4) How can you determine if two shapes are similar?
Two shapes are similar if corresponding angles are congruent and the corresponding side lengths are proportional.
5) True or False: If two shapes are similar, their corresponding angles are congruent.
True. Similar shapes have corresponding angles that are congruent.
6) In a triangle ABC, angle A measures 40 degrees, angle B measures 70 degrees, and angle C measures 70 degrees. Is triangle ABC similar to a triangle with angle measures 80 degrees, 50 degrees, and 50 degrees? If so, explain why.
Yes, triangle ABC is similar to the triangle with angle measures 80 degrees, 50 degrees, and 50 degrees. This is because corresponding angles are congruent: angle A corresponds to the 80-degree angle, angle B corresponds to the 50-degree angle, and angle C corresponds to the other 50-degree angle.
7) In a rectangle with side lengths of 6 and 8, if the length is doubled and the width is tripled, is the resulting shape similar to the original rectangle? If so, explain why.
Yes, the resulting shape is similar to the original rectangle. This is because corresponding side lengths are proportional: the length doubled from 6 to 12, and the width tripled from 8 to 24, maintaining the same ratio between the sides (2:3).
8) What is the relationship between the areas of two similar figures?
The relationship between the areas of two similar figures is that they are proportional to the square of the ratio of corresponding side lengths.