Pythagorean Theorem and its Converse

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 is expressed as a² + b² = c².

Front

What type of triangle is formed by the sides 6, 8, and 12?

Back

Obtuse triangle.

Front

What is the condition for a triangle to be classified as a right triangle?

Back

A triangle is a right triangle if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides.

Front

If a triangle has sides of lengths 4, 5, and 6, what type of triangle is it?

Back

Acute triangle.

Front

Can sticks of lengths 10cm, 11cm, and 13cm form a right triangle?

Back

No, because 10² + 11² does not equal 13² (100 + 121 ≠ 169).

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

If a triangle has sides of lengths 2.1, 7.2, and 7.5, is it a right triangle?

Back

Yes, it is a right triangle.

Front

What is an acute triangle?

Back

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

Front

What is an obtuse triangle?

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the length of the hypotenuse is always greater than either of the other two sides.