Day 7 HW- Converse of the Pythagorean Theorem

Front

What is the Converse of the Pythagorean Theorem?

Back

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

What are the side lengths of a right triangle?

Back

The side lengths of a right triangle are the two legs (shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

How can you determine if a set of three lengths can form a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Front

What is a hypotenuse?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If the sides of a triangle are 5, 12, and 13, is it a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the relationship between the angles in a right triangle?

Back

The sum of the angles in any triangle is 180 degrees, and in a right triangle, one angle is always 90 degrees.

Front

What does it mean for a triangle to be acute?

Back

An acute triangle has all three angles measuring less than 90 degrees.

Front

What does it mean for a triangle to be obtuse?

Back

An obtuse triangle has one angle measuring more than 90 degrees.

Front

Can a triangle have two right angles?

Back

No, a triangle cannot have two right angles because the sum of angles would exceed 180 degrees.

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) * base * height.