Triangle Inequality Theorem

A The sum of the lengths of any two sides of a triangle is less than the length of the third side.

B The sum of the lengths of any two sides of a triangle is equal to the length of the third side.

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

D The sum of the lengths of any two sides of a triangle is greater than or equal to the length of the third side.

A The dashed red line and the courtyard walkway determine three sides of a triangle, so by the Triangle Inequality Theorem, the path that follows the dashed red line is shorter or equal to the courtyard walkway.

B The dashed red line and the courtyard walkway determine three sides of a triangle, so by the Triangle Inequality Theorem, the path that follows the dashed red line is equal to than the courtyard walkway.

C The dashed red line and the courtyard walkway determine three sides of a triangle, so by the Triangle Inequality Theorem, the path that follows the dashed red line is shorter than the courtyard walkway.

D The dashed red line and the courtyard walkway determine three sides of a triangle, so by the Triangle Inequality Theorem, the path that follows the dashed red line is longer than the courtyard walkway.

A The sign, Topeka, and Wichita are collinear. If D is the distance between Topeka and Wichita, then

B The sign, Topeka, and Wichita determine the vertices of a triangle. If D is the distance between Topeka and Wichita, then

C The sign, Topeka, and Wichita determine the vertices of a triangle. If D is the distance between Topeka and Wichita, then

D The sign, Topeka, and Wichita determine the vertices of a triangle. If D is the distance between Topeka and Wichita, then

A No because the sum of the lengths of the two shorter sides is equal to the length of the third​ side, and this contradicts the triangle inequality theorem.

B No because the sum of the lengths of the two shorter sides is less than the length of the third​ side, and this contradicts the triangle inequality theorem.

C Yes because the sum of the lengths of any two sides is greater than the length of the third​ side, and this satisfies the triangle inequality theorem.

D Yes because the sum of the lengths of any two sides is less than the length of the third​ side, and this satisfies the triangle inequality theorem.

A No because the sum of the lengths of the two shorter sides is greater than the length of the third​ side, and this contradicts the triangle inequality theorem.

B No because the sum of the lengths of the two shorter sides is less than the length of the third​ side, and this contradicts the triangle inequality theorem.

C Yes because the sum of the lengths of any two sides is greater than the length of the third​ side, and this satisfies the triangle inequality theorem.

D Yes because the sum of the lengths of any two sides is less than the length of the third​ side, and this satisfies the triangle inequality theorem.

A No because the sum of the lengths of the two shorter sides is greater than the length of the third​ side, and this contradicts the triangle inequality theorem.

B No because the sum of the lengths of the two shorter sides is less than the length of the third​ side, and this contradicts the triangle inequality theorem.

C Yes because the sum of the lengths of any two sides is greater than the length of the third​ side, and this satisfies the triangle inequality theorem.

D Yes because the sum of the lengths of any two sides is less than the length of the third​ side, and this satisfies the triangle inequality theorem.

A Yes because the sum of the lengths of any two sides is greater than the length of the third​ side, and this satisfies the triangle inequality theorem.

B Yes because the sum of the lengths of any two sides is greater than or equal to the length of the third​ side, and this satisfies the triangle inequality theorem.

C No because the sum of the lengths of the two shorter sides is less than the length of the third​ side, and this contradicts the triangle inequality theorem.

D No because the sum of the lengths of the two shorter sides is equal to the length of the third​ side, and this contradicts the triangle inequality theorem.

A No, because 4 + 9 < 15 contradicts the triangle inequality theorem.

B No, because 9 + 15 > 4 contradicts the triangle inequality theorem.

C Yes, because 9 + 15 > 4 satisfies the triangle inequality theorem.

D Yes, because 4 + 9 < 15 satisfies the triangle inequality theorem.

A No, because 3 + 5 > 1 contradicts the triangle inequality theorem.

B No, because 1 +3 < 5 contradicts the triangle inequality theorem.

C Yes, because 3 + 5 > 1 satisfies the triangle inequality theorem.

D Yes, because 1 + 3 < 5 satisfies the triangle inequality theorem.

A No, because 8 + 10 < 6 contradicts the triangle inequality theorem.

B No, because 6 + 8 < 10 contradicts the triangle inequality theorem.

C Yes, because 8 + 10 > 6 satisfies the triangle inequality theorem.

D Yes, because 6 + 8 > 10 satisfies the triangle inequality theorem.

A No, because 2 + 3 > 6 contradicts the triangle inequality theorem.

B No, because 2 + 3 < 6 contradicts the triangle inequality theorem.

C Yes, because 2 + 3 > 6 satisfies the triangle inequality theorem.

D Yes, because 2 + 3 < 6 satisfies the triangle inequality theorem.

A

B

C

D

A

B

C

D

A 8, 22

B 7, 23

C 6, 24

D 5, 20

A 0, 36

B 1, 35

C 1, 37

D 2, 38

A 13

B 14

C 15

D 16

A 5

B 6

C 7

D 8

A 2, 8, 8

B 4, 7, 7

C 5, 5, 8

D 6, 6, 6

E 0, 9, 9

A 5 and 9

B 5 and 15

C 9 and 15

D 9 and 19

E 15 and 19

A 299 ft

B 300 ft

C 599 ft

D 600 ft

A

B

C

D