Day 8 HW Converse Pythagorean Theorem

Front

What is the Converse Pythagorean Theorem?

Back

If a triangle has sides of lengths a, b, and c, and a^2 + b^2 = c^2, then the triangle is a right triangle.

Front

What is a right triangle?

Back

A triangle that has one angle measuring 90 degrees.

Front

What are the conditions for three lengths to form a triangle?

Back

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

Front

Can the lengths 7, 10, and 8 form a triangle?

Back

Yes, because 7 + 8 > 10, 7 + 10 > 8, and 8 + 10 > 7.

Front

What is the formula to check if a triangle is a right triangle using the Pythagorean theorem?

Back

c^2 = a^2 + b^2, where c is the longest side.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, because 5^2 + 12^2 = 13^2 (25 + 144 = 169).

Front

What does it mean if a triangle is not a right triangle?

Back

It means that the square of the longest side is not equal to the sum of the squares of the other two sides.

Front

What is the significance of the longest side in a triangle?

Back

The longest side is always opposite the largest angle in the triangle.

Front

Can the lengths 10, 6, and 8 form a right triangle?

Back

No, because 10^2 is not equal to 6^2 + 8^2 (100 ≠ 36 + 64).

Front

What is the relationship between the angles and sides in a triangle?

Back

In a triangle, the larger the angle, the longer the side opposite that angle.