Similar shapes

Front

What does it mean for two shapes to be similar?

Back

Two shapes are similar if they have the same shape but may differ in size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Front

Are all squares similar?

Back

Yes, all squares are similar because they all have four equal sides and four right angles.

Front

Are all hexagons similar?

Back

No, not all hexagons are similar. Hexagons can have different side lengths and angles.

Front

Are all scalene triangles similar?

Back

No, scalene triangles are not similar because they have different side lengths and angles.

Front

What is the relationship between the lengths of shadows of similar objects?

Back

The lengths of the shadows of similar objects are proportional to their heights.

Front

If a student who is 4 feet tall casts a shadow of 6 feet, and a tree casts a shadow of 12 feet, how do you find the height of the tree?

Back

Use the proportion: height of student / shadow of student = height of tree / shadow of tree. So, 4/6 = height of tree / 12. Solving gives height of tree = 8 feet.

Front

What is the formula for finding the height of similar triangles?

Back

The formula is: (height of triangle 1 / base of triangle 1) = (height of triangle 2 / base of triangle 2).

Front

If two triangles are similar, what can you say about their angles?

Back

If two triangles are similar, their corresponding angles are equal.

Front

If the sides of two similar shapes are in the ratio 2:3, what is the ratio of their areas?

Back

The ratio of their areas will be the square of the ratio of their sides, so (2:3)² = 4:9.

Front

What is a scale factor in similar shapes?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar shapes.