Right Triangles

Front

What is a right triangle?

Back

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

Tags

CCSS.4.G.A.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 (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Tags

CCSS.8.G.B.7

Front

What are the side ratios in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the ratios of the lengths of the sides opposite the 30°, 60°, and 90° angles are 1:√3:2.

Tags

CCSS.8.G.B.8

Front

What are the side ratios in a 45-45-90 triangle?

Back

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

Tags

CCSS.8.G.B.8

Front

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

Back

To find the length of the hypotenuse, use the Pythagorean theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Tags

CCSS.8.G.B.7

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Tags

CCSS.4.G.A.2

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Tags

CCSS.4.G.A.2

Front

What is the relationship between the sides of a triangle?

Back

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If a triangle has sides of lengths 10, 18, and 40, what type of triangle is it?

Back

It is not a triangle because the sum of the lengths of the two shorter sides (10 + 18) is less than the length of the longest side (40).

Tags

CCSS.7.G.A.2

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

Use the Pythagorean theorem: if a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Tags

CCSS.8.G.B.8