Similar Triangles Applications

Front

What are similar triangles?

Back

Similar triangles are triangles 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 principle of proportionality in similar triangles?

Back

The principle of proportionality states that in similar triangles, the ratios of the lengths of corresponding sides are equal.

Front

How can you find the height of an object using similar triangles?

Back

To find the height of an object using similar triangles, set up a proportion between the height of the object and the length of its shadow, compared to the height of a reference object and its shadow.

Front

If a 2-meter tall person casts a shadow of 1 meter, what is the ratio of height to shadow length?

Back

The ratio of height to shadow length is 2:1.

Front

In a problem involving similar triangles, if a tree casts a shadow of 12 meters and a person casts a shadow of 1.5 meters, how do you set up the proportion?

Back

Set up the proportion as: height of tree / 12 = height of person / 1.5.

Front

What is the height of a flagpole if a 3-meter tall person casts a shadow of 2 meters and the flagpole casts a shadow of 15 meters?

Back

The height of the flagpole is 22.5 meters.

Front

How do you calculate the height of a ladder leaning against a wall using the Pythagorean theorem?

Back

Use the formula: height^2 + base^2 = ladder length^2. For a ladder of 12 meters and base of 10 meters, height = sqrt(12^2 - 10^2).

Front

What is the height of a flagpole if it casts a shadow of 10 meters and a 2-meter tall person casts a shadow of 1 meter?

Back

The height of the flagpole is 20 meters.

Front

What is the relationship between the lengths of shadows and the heights of objects in similar triangles?

Back

The lengths of shadows are proportional to the heights of the objects casting them.

Front

If a tree is 16 meters tall and casts a shadow of 12 meters, what is the height of a 2-meter tall person casting a shadow of 1.5 meters?

Back

The height of the person is 2 meters.