Scale Factor

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In geometry, it is the ratio of the lengths of corresponding sides of two similar figures.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the relationship between corresponding angles in similar figures?

Back

All corresponding angles in similar figures are congruent.

Front

If the scale factor is 3, how do you find the length of a side in the scaled figure if the original side is 5 m?

Back

Multiply the original side length by the scale factor: 5 m * 3 = 15 m.

Front

How do you determine the scale factor between two similar triangles?

Back

To determine the scale factor, divide the length of a side of one triangle by the length of the corresponding side of the other triangle.

Front

What is the scale factor from triangle ABC to triangle DEF if the sides of ABC are 4 m, 6 m, and 8 m, and the corresponding sides of DEF are 8 m, 12 m, and 16 m?

Back

The scale factor is 2, as each side of triangle DEF is twice the length of the corresponding side of triangle ABC.

Front

If a triangle is scaled by a factor of 0.5, what happens to the area of the triangle?

Back

The area of the triangle is scaled by the square of the scale factor. So, if the scale factor is 0.5, the area is scaled by (0.5)^2 = 0.25, meaning the area is reduced to 25% of the original area.

Front

What is the corresponding side length to side EF in triangle LMN if the scale factor from triangle LMN to triangle DEF is 2?

Back

The corresponding side length to EF in triangle LMN is half the length of EF.

Front

How do you find the corresponding side length in a scaled figure?

Back

To find the corresponding side length in a scaled figure, multiply the original side length by the scale factor.

Front

What is the significance of congruent angles in similar figures?

Back

Congruent angles ensure that the figures maintain their shape, which is essential for the figures to be classified as similar.