Wednesday - Similar Triangle Word Problems

Front

What is the concept of 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

How do you set up a proportion to solve for an unknown height using similar triangles?

Back

To set up a proportion, you can use the ratio of the heights of the objects to the lengths of their shadows. For example, if a pole's height is to its shadow length as a building's height is to its shadow length, you can write: (height of pole)/(shadow of pole) = (height of building)/(shadow of building).

Front

If a 10 m tall pole casts an 8 m shadow, what is the height of a building that casts a 14 m shadow?

Back

Using the proportion: (10 m / 8 m) = (height of building / 14 m). Solving gives height of building = 17.5 m.

Front

What is the formula for finding the height of an object using similar triangles?

Back

The formula is: height of object = (height of known object * length of shadow of unknown object) / length of shadow of known object.

Front

What does it mean if two triangles are similar?

Back

It means that their corresponding angles are equal and their corresponding sides are in proportion.

Front

How can you determine if two triangles are similar?

Back

You can determine if two triangles are similar by checking if their corresponding angles are equal (Angle-Angle criterion) or if the lengths of their sides are proportional (Side-Side-Side criterion).

Front

What is the significance of the shadow length in similar triangle problems?

Back

The shadow length is significant because it provides a proportional relationship between the heights of the objects and their respective shadow lengths, allowing for the calculation of unknown heights.

Front

If a tree casts a shadow of 4 m and is 16 ft tall, what is the height of another tree that casts a shadow of 2 m?

Back

Using the proportion: (16 ft / 4 m) = (height of second tree / 2 m). Solving gives height of second tree = 8 ft.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

How do you find the unknown side of a triangle using similar triangles?

Back

You can find the unknown side by setting up a proportion based on the lengths of the corresponding sides of the similar triangles.