7.5a indirect measurement

Front

What is indirect measurement?

Back

Indirect measurement is a technique used to measure an object’s height or distance without directly measuring it, often using proportions and similar triangles.

Front

How do you set up a proportion for indirect measurement?

Back

To set up a proportion, you compare the ratios of corresponding sides of similar figures. For example, if two triangles are similar, the ratio of their heights is equal to the ratio of their bases.

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

32 feet.

Front

What are corresponding angles?

Back

Corresponding angles are angles that are in the same position in different shapes or figures that are similar.

Front

True or False: Sides in similar figures must be proportional.

Back

True.

Front

If a flagpole is represented as 1 inch = 4 feet, how tall is a 12-inch flagpole in reality?

Back

48 feet.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but different sizes, meaning their corresponding angles are equal and their sides are proportional.

Front

What is the relationship between the lengths of shadows and the heights of objects in indirect measurement?

Back

The lengths of shadows and the heights of objects are proportional to each other when the light source is the same.

Front

If a triangle has sides of lengths 3, 4, and 5, what is the ratio of its sides to a similar triangle with sides of lengths 6, 8, and 10?

Back

The ratio is 1:2.

Front

What is a scale factor in similar figures?

Back

A scale factor is the ratio of the lengths of corresponding sides of two similar figures.