Indirect Measurement

Front

What is Indirect Measurement?

Back

Indirect measurement is a technique used to determine the length or height of an object without measuring it directly, often using similar triangles and proportions.

Front

What is a proportion in the context of indirect measurement?

Back

A proportion is an equation that states that two ratios are equal, often used to set up relationships between corresponding sides of similar triangles.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the formula for finding the length of a side in similar triangles?

Back

If triangle A and triangle B are similar, then the ratio of the lengths of corresponding sides is equal: (side A1 / side A2) = (side B1 / side B2).

Front

If two triangles have sides of lengths 3 and 5, and the corresponding side of the second triangle is 15, what is the length of the corresponding side of the first triangle?

Back

The length of the corresponding side of the first triangle is 9, calculated using the proportion: (3/5) = (x/15) => x = 9.

Front

What is the significance of the scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of similar triangles, indicating how much larger or smaller one triangle is compared to the other.

Front

How can you use shadows to measure the height of a tree indirectly?

Back

By measuring the length of the shadow of the tree and a known height object, you can set up a proportion to find the height of the tree.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal, which is a key property used to establish similarity.

Front

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE are 4 and 8 respectively, what is the scale factor?

Back

The scale factor is 2, calculated as 8/4.

Front

What is the first step in solving an indirect measurement problem?

Back

The first step is to identify the similar triangles and set up a proportion based on their corresponding sides.