Nested Triangles

Front

What are nested triangles?

Back

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

Front

What is the property of similar triangles?

Back

Similar triangles have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

How do 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 heights and the lengths of the shadows.

Front

If triangle A is similar to triangle B, and the sides of triangle A are 4 cm, 6 cm, and 8 cm, what are the corresponding sides of triangle B if the scale factor is 2?

Back

The corresponding sides of triangle B would be 8 cm, 12 cm, and 16 cm.

Front

What is the formula for finding the area of a triangle?

Back

The area of a triangle is given by the formula: Area = 1/2 * base * height.

Front

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, is it a right triangle?

Back

Yes, it is a right triangle because it follows the Pythagorean theorem: 3^2 + 4^2 = 5^2.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

How do you solve for an unknown side in similar triangles?

Back

To solve for an unknown side in similar triangles, set up a proportion using the lengths of the corresponding sides.

Front

If a 10-foot tall statue casts a shadow of 5 feet, what is the height of a 30-foot tall tree that casts a shadow of x feet?

Back

Using proportions, x = (30 * 5) / 10 = 15 feet.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.