Triangles and Inequalities HW

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If the lengths of two sides of a triangle are 5 and 7, what is the range of possible lengths for the third side?

Back

The range of possible lengths for the third side is between 2 and 12 (i.e., 2 < x < 12).

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Tags

CCSS.4.G.A.2

Front

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

Back

Use the Pythagorean theorem: if a^2 + b^2 = c^2, where c is the longest side, then the lengths can form a right triangle.

Tags

CCSS.8.G.B.8

Front

Do the lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9^2 + 12^2 = 15^2 (81 + 144 = 225).

Tags

CCSS.8.G.B.8

Front

Do the lengths 13, 80, and 81 form a right triangle?

Back

No, because 13^2 + 80^2 ≠ 81^2 (169 + 6400 ≠ 6561).

Tags

CCSS.8.G.B.8

Front

What is the range of possible values for x if the triangle sides are 2, x, and 6?

Back

The range is 4 < x < 8.

Front

What does it mean for line segments to be able to form a triangle?

Back

It means that the lengths of the segments must satisfy the Triangle Inequality Theorem.

Front

If x > 2, what can you conclude about the triangle formed by sides x, 2, and 3?

Back

The segments can form a triangle since 2 + 3 > x.

Tags

CCSS.7.G.A.2

Front

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

Back

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

Tags

CCSS.HSG.CO.C.10