Similarity / Right Triangles

Front

What is similarity in geometry?

Back

Similarity in geometry refers to the relationship between two shapes that have the same shape but may differ in size. Corresponding angles are equal, and corresponding sides are proportional.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

What are the properties of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the legs are of equal length, and the length of the hypotenuse is √2 times the length of each leg.

Front

What are the properties of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is the longest side.

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, you can use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

What is an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.

Front

What is the relationship between the angles in similar triangles?

Back

In similar triangles, corresponding angles are equal.

Front

How do 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 proportional.