Unit 5: Triangle and Pythagorean Inequality Theorems

Front

Can these lengths form a triangle? 21, 7, 12

Back

No, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

State if the 3 sides form an acute, obtuse, or right triangle. 6, 8, 10

Back

Right triangle, because 6² + 8² = 10².

Front

State if the 3 sides form an acute, obtuse, or right triangle. 3.6, 7.4, 8.5

Back

Obtuse triangle, because 3.6² + 7.4² < 8.5².

Front

State if the 3 sides form an acute, obtuse, or right triangle. 13, 16.8, 21

Back

Acute triangle, because 13² + 16.8² > 21².

Front

State if the 3 sides form an acute, obtuse, or right triangle. 6.6, 11.2, 13

Back

Right triangle, because 6.6² + 11.2² = 13².

Front

What is the Triangle Inequality Theorem?

Back

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

Front

What defines an acute triangle?

Back

An acute triangle has all angles less than 90 degrees.

Front

What defines an obtuse triangle?

Back

An obtuse triangle has one angle greater than 90 degrees.

Front

What defines a right triangle?

Back

A right triangle has one angle equal to 90 degrees.

Front

How do you determine if a triangle is acute, obtuse, or right using side lengths?

Back

Use the Pythagorean theorem: a² + b² = c² for right triangles; a² + b² > c² for acute; a² + b² < c² for obtuse.