GEO - Pythagorean 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). Formula: a² + b² = c².

Front

What is an acute triangle?

Back

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

Front

What is an obtuse triangle?

Back

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

Front

What is a right triangle?

Back

A right triangle is a triangle that has one interior angle equal to 90 degrees.

Front

What is the triangle inequality theorem?

Back

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

Front

How can you determine if three sides can form a triangle?

Back

To determine if three sides can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side for all three combinations.

Front

What are the conditions for a triangle to be classified as acute, right, or obtuse?

Back

1. Acute: a² + b² > c²; 2. Right: a² + b² = c²; 3. Obtuse: a² + b² < c², where c is the longest side.

Front

Given sides 9.6, 20.1, 18, what type of triangle do they form?

Back

They form an acute triangle.

Front

Given sides 6, 4, 5, what type of triangle do they form?

Back

They form an acute triangle.

Front

Given sides 3, 4, 10, do they form a triangle?

Back

No, they do not form a triangle.