Triangle Inequality Theorem

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In your own words, describe what it takes to form a triangle.

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You and a friend compete in a scavenger hunt at a museum. The two of you walk from the Picasso exhibit to the Native American gallery along the dashed red line. When he sees that another team is ahead of you, your friend says, “They must have cut through the courtyard.” Explain what your friend means.

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Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 in, 20 in, 30 in

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Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
5 ft, 14 ft, 7 ft

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Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
6 m, 6 m, 11 m

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Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
9 cm, 9 cm, 18 cm

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Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
4 yds, 9 yds, 15 yds

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Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
1 mi, 5 mi, 3 mi

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Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 km, 8 km, 6 km

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Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
2 in, 3 in, 6 in

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A triangle has two sides of length 7, and 11. The third side must be greater than __ and less than _.

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A triangle has two sides of length 15 and 8. The third side must be greater than and less than .

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A leg of an isosceles triangle is 18. The length of the base must be greater than and less than _.

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If the sum of the lengths of two sides of a triangle is 15, what is the largest possible integral value for the length of the third side?

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If the base of an isosceles triangle has a length of 10, what is the shortest possible integral value for the length of each of the congruent sides?

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The perimeter of a triangle is 18 inches. If the length of each side is an integer, what length combinations will not form an isosceles triangle?

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A triangle with one side 3 and another side 7 has perimeter P. What are the least and greatest possible integer values of P?

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You are enclosing a triangular playground with fence. You have measured two sides of the playground to be 100 feet and 200 feet. What is the maximum total length of fence that you need?

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G.9-12.5.D

Triangle Inequality Theorem

In your own words, describe what it takes to form a triangle.

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 in, 20 in, 30 in

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
5 ft, 14 ft, 7 ft

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
6 m, 6 m, 11 m

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
9 cm, 9 cm, 18 cm

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
4 yds, 9 yds, 15 yds

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
1 mi, 5 mi, 3 mi

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 km, 8 km, 6 km

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
2 in, 3 in, 6 in

A triangle has two sides of length 7, and 11. The third side must be greater than __ and less than _.

A triangle has two sides of length 15 and 8. The third side must be greater than and less than .

A leg of an isosceles triangle is 18. The length of the base must be greater than and less than _.

If the sum of the lengths of two sides of a triangle is 15, what is the largest possible integral value for the length of the third side?

If the base of an isosceles triangle has a length of 10, what is the shortest possible integral value for the length of each of the congruent sides?

The perimeter of a triangle is 18 inches. If the length of each side is an integer, what length combinations will not form an isosceles triangle?

A triangle with one side 3 and another side 7 has perimeter P. What are the least and greatest possible integer values of P?

You are enclosing a triangular playground with fence. You have measured two sides of the playground to be 100 feet and 200 feet. What is the maximum total length of fence that you need?

In your own words, describe what it takes to form a triangle.

Your family drives across Kansas on Interstate 70. A sign reads, “Wichita 90 mi, Topeka 110 mi.” Your little brother says, “I didn’t know that it was only 20 miles from Wichita to Topeka.” Explain why the distance between the two cities does not have to be 20 mi.

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 in, 20 in, 30 in

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
5 ft, 14 ft, 7 ft

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
6 m, 6 m, 11 m

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
9 cm, 9 cm, 18 cm

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
4 yds, 9 yds, 15 yds

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
1 mi, 5 mi, 3 mi

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 km, 8 km, 6 km

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
2 in, 3 in, 6 in

Write an inequality to show possible values of x.

Write an inequality to show possible values of x.

A triangle has two sides of length 7, and 11. The third side must be greater than __ and less than _.

A triangle has two sides of length 15 and 8. The third side must be greater than and less than .

A leg of an isosceles triangle is 18. The length of the base must be greater than and less than _.

If the sum of the lengths of two sides of a triangle is 15, what is the largest possible integral value for the length of the third side?

If the base of an isosceles triangle has a length of 10, what is the shortest possible integral value for the length of each of the congruent sides?

The perimeter of a triangle is 18 inches. If the length of each side is an integer, what length combinations will not form an isosceles triangle?

A triangle with one side 3 and another side 7 has perimeter P. What are the least and greatest possible integer values of P?

You are enclosing a triangular playground with fence. You have measured two sides of the playground to be 100 feet and 200 feet. What is the maximum total length of fence that you need?

Use the inequality: AB + BC > AC to set up and solve a relationship between the sides of the triangle.

Triangle Inequality Theorem

Triangle Inequality Theorem

In your own words, describe what it takes to form a triangle.

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.10 in, 20 in, 30 in

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.5 ft, 14 ft, 7 ft

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.6 m, 6 m, 11 m

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.9 cm, 9 cm, 18 cm

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.4 yds, 9 yds, 15 yds

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.1 mi, 5 mi, 3 mi

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.10 km, 8 km, 6 km

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.2 in, 3 in, 6 in

A triangle has two sides of length 7, and 11. The third side must be greater than ________ and less than _______.

A triangle has two sides of length 15 and 8. The third side must be greater than ________ and less than ________.

A leg of an isosceles triangle is 18. The length of the base must be greater than ________ and less than _________.

If the sum of the lengths of two sides of a triangle is 15, what is the largest possible integral value for the length of the third side?

If the base of an isosceles triangle has a length of 10, what is the shortest possible integral value for the length of each of the congruent sides?

The perimeter of a triangle is 18 inches. If the length of each side is an integer, what length combinations will not form an isosceles triangle?

A triangle with one side 3 and another side 7 has perimeter P. What are the least and greatest possible integer values of P?

You are enclosing a triangular playground with fence. You have measured two sides of the playground to be 100 feet and 200 feet. What is the maximum total length of fence that you need?

In your own words, describe what it takes to form a triangle.

Your family drives across Kansas on Interstate 70. A sign reads, “Wichita 90 mi, Topeka 110 mi.” Your little brother says, “I didn’t know that it was only 20 miles from Wichita to Topeka.” Explain why the distance between the two cities does not have to be 20 mi.

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.10 in, 20 in, 30 in

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.5 ft, 14 ft, 7 ft

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.6 m, 6 m, 11 m

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.9 cm, 9 cm, 18 cm

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.4 yds, 9 yds, 15 yds

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.1 mi, 5 mi, 3 mi

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.10 km, 8 km, 6 km

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.2 in, 3 in, 6 in

Write an inequality to show possible values of x.

Write an inequality to show possible values of x.

A triangle has two sides of length 7, and 11. The third side must be greater than ________ and less than _______.

A triangle has two sides of length 15 and 8. The third side must be greater than ________ and less than ________.

A leg of an isosceles triangle is 18. The length of the base must be greater than ________ and less than _________.

If the sum of the lengths of two sides of a triangle is 15, what is the largest possible integral value for the length of the third side?

If the base of an isosceles triangle has a length of 10, what is the shortest possible integral value for the length of each of the congruent sides?

The perimeter of a triangle is 18 inches. If the length of each side is an integer, what length combinations will not form an isosceles triangle?

A triangle with one side 3 and another side 7 has perimeter P. What are the least and greatest possible integer values of P?

You are enclosing a triangular playground with fence. You have measured two sides of the playground to be 100 feet and 200 feet. What is the maximum total length of fence that you need?

Use the inequality: AB + BC > AC to set up and solve a relationship between the sides of the triangle.

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 in, 20 in, 30 in

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
5 ft, 14 ft, 7 ft

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
6 m, 6 m, 11 m

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
9 cm, 9 cm, 18 cm

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
4 yds, 9 yds, 15 yds

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
1 mi, 5 mi, 3 mi

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 km, 8 km, 6 km

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
2 in, 3 in, 6 in

A triangle has two sides of length 7, and 11. The third side must be greater than __ and less than _.

A triangle has two sides of length 15 and 8. The third side must be greater than and less than .

A leg of an isosceles triangle is 18. The length of the base must be greater than and less than _.

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 in, 20 in, 30 in

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
5 ft, 14 ft, 7 ft

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
6 m, 6 m, 11 m

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
9 cm, 9 cm, 18 cm

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
4 yds, 9 yds, 15 yds

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
1 mi, 5 mi, 3 mi

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
10 km, 8 km, 6 km

Determine if the set of numbers could represent the lengths of the sides of a triangle. Explain.
2 in, 3 in, 6 in

A triangle has two sides of length 7, and 11. The third side must be greater than __ and less than _.

A triangle has two sides of length 15 and 8. The third side must be greater than and less than .

A leg of an isosceles triangle is 18. The length of the base must be greater than and less than _.