Similar Figures and Indirect measure

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 their corresponding sides are in proportion.

Front

What is the principle of indirect measurement?

Back

Indirect measurement is a technique used to measure distances or heights that are difficult to measure directly, often using similar triangles.

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

The lengths of their corresponding sides are proportional.

Front

How do you find the length of a missing side in similar triangles?

Back

Use the proportion of the lengths of corresponding sides to set up a ratio and solve for the missing length.

Front

What is the formula for finding the scale factor between two similar figures?

Back

Scale factor = Length of a side of the larger figure / Length of the corresponding side of the smaller figure.

Front

If triangle ABC is similar to triangle DEF, and AB = 4 cm, DE = 8 cm, what is the scale factor?

Back

The scale factor is 2:1.

Front

In similar triangles, if one triangle has a side length of 10 cm and the corresponding side in the other triangle is 15 cm, what is the ratio of their areas?

Back

The ratio of their areas is (10^2):(15^2) = 100:225 = 4:9.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

How can you use similar triangles to measure the height of a tree?

Back

By creating a right triangle with a known height and distance, you can use the properties of similar triangles to find the height of the tree.

Front

If triangle CDE is similar to triangle CBA, and CD = 5 m, what is the corresponding side in triangle CBA if the scale factor is 3:1?

Back

The corresponding side in triangle CBA is 15 m.