Triangle Inequalities and Hinge Theorem

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

Can a triangle exist with side lengths 15, 12, and 9?

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

Tags

CCSS.7.G.A.2

Front

What does the Hinge Theorem state?

Back

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angles are not equal, then the longer side is opposite the larger angle.

Front

If AB = 5 and AC = 7, what can we say about the length of BC if angle A is larger than angle B?

Back

BC is greater than 5.

Front

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

Back

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

Tags

CCSS.HSG.CO.C.10

Front

Can the sides of a triangle have lengths 3, 8, and 9?

Back

Yes, because 3 + 8 > 9, 3 + 9 > 8, and 8 + 9 > 3.

Tags

CCSS.7.G.A.2

Front

Which side is longer in triangle ABC if AB = 6, AC = 10, and angle A is the largest angle?

Back

AC is longer than AB.

Tags

CCSS.HSG.CO.C.10

Front

What is the minimum length of the third side of a triangle if the other two sides are 7 and 10?

Back

The minimum length of the third side must be greater than 3 (10 - 7).

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.

Tags

CCSS.4.G.A.2

Front

What is the maximum length of the third side of a triangle if the other two sides are 5 and 12?

Back

The maximum length of the third side must be less than 17 (5 + 12).