Similar Figures and Indirect Measures

Front

What are similar figures?

Back

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

Front

What is the scale factor?

Back

The scale factor is a ratio that compares the lengths of corresponding sides of two similar figures. It indicates how much one figure has been enlarged or reduced compared to the other.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and the ratios of the lengths of their corresponding sides are equal.

Front

What is indirect measurement?

Back

Indirect measurement is a technique used to measure an object that is difficult to measure directly, often using similar figures and proportions.

Front

If a home's height is 40 ft and casts a shadow of 12 ft, what is the height of a car that casts a shadow of 3 ft?

Back

The height of the car is 10 ft.

Front

What is the relationship between the heights and shadows of similar figures?

Back

The ratio of the heights of two similar figures is equal to the ratio of their corresponding shadows.

Front

What does it mean for two figures to be proportional?

Back

Two figures are proportional if their corresponding sides have the same ratio, meaning they can be scaled versions of each other.

Front

If triangle ABC is similar to triangle DEF, and the length of AB is 6 cm and DE is 9 cm, what is the scale factor from triangle ABC to triangle DEF?

Back

The scale factor is 3/2.

Front

What is the formula for finding the height of an object using indirect measurement with a mirror?

Back

Height of the object = (Distance to the mirror) x (Height of the observer) / (Distance from the observer to the mirror).

Front

If two triangles have side lengths of 4 cm, 6 cm, and 8 cm, and 2 cm, 3 cm, and 4 cm respectively, are they similar?

Back

Yes, they are similar because the ratios of the corresponding sides are equal (4:2, 6:3, 8:4 all equal 2:1).