Triangle Inequalities & Hinge Theorem

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

• Yes
• No

Tags

CCSS.7.G.A.2

Does a triangle with these side lengths exist?
15, 12, 9

• Yes
• No
• I don't know.

Tags

CCSS.7.G.A.2

What is a possible third side to a triangle with side lengths of 13 and 4?

• 9
• 12
• 8
• 5

Tags

CCSS.7.G.A.2

Which of the following would NOT work to make a triangle with the two side lengths of 2 and 6?

• 6
• 7
• 5
• 4

Tags

CCSS.7.G.A.2

Name the smallest angle in this triangle.

• ∠A
• ∠B
• ∠C

Tags

CCSS.HSG.CO.C.10

Two sides of a triangle have side lengths of 17 meters and 12 meters.  What is the range of possible lengths for the third side?

• 12 < x < 17
• 12 < x < 29
• 5 < x < 17
• 5 < x < 29

Which set of numbers may represent the lengths of the sides of a triangle?

• {2, 5, 9}

• {6, 6, 7}

• {6, 4, 2}

• {7, 8, 1}

Tags

CCSS.7.G.A.2

Two sides of a triangle have side lengths of 12 meters and 7 meters. What is the range of possible lengths for the third side?

• 12 < x < 19

• 5 < x < 29

• 5 < x < 19

• 7 < x < 12

It is called the HINGE theorem, because...

• the vertex of the angle acts like a hinge to open the triangle.

• it's named after Joseph Hinge, the man who discovered it.

• "hinge" is the Spanish word for angle.

• the triangle makes a hinge shape, like a tent.

Compare QT and ST

Tags

CCSS.HSG.CO.C.9