Nested Triangles

Front

What are nested triangles?

Back

Nested triangles are triangles that are contained within one another, sharing a common vertex and having proportional sides.

Front

What is the principle of similar triangles?

Back

Similar triangles 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 find the height of an object using shadows?

Back

You can use the ratio of the height of the object to the length of its shadow, which is equal to the ratio of the height of another object to the length of its shadow.

Front

If a 6-foot tall person casts a shadow that is 4 feet long, what is the height of a building that casts a 60-foot long shadow?

Back

90 feet

Front

If a 5-foot tall pole casts a shadow that is 10 feet long, what is the height of a nearby tree if its shadow is 25 feet long?

Back

12.5 feet

Front

What is the formula to find the height of an object using similar triangles?

Back

Height of object = (Height of known object / Length of known shadow) * Length of unknown shadow.

Front

If a 8-foot tall statue casts a shadow that is 6 feet long, what is the height of a tree that casts a 24-foot long shadow?

Back

32 feet

Front

What does it mean for triangles to be proportional?

Back

Triangles are proportional when the ratios of their corresponding sides are equal.

Front

How can you determine if two triangles are similar?

Back

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

Front

What is the relationship between the height of an object and the length of its shadow?

Back

The height of an object is directly proportional to the length of its shadow when the light source is at the same angle.