TRIANGLE INEQUALITIES THEOREMS

What theorem that states, “If one side of a triangle is longer than the second side, then the angle opposite to the first side is larger than the angle opposite the second side.”?

• Triangle Inequality Theorem 1 (Ss --> Aa)

• B. Triangle Inequality Theorem 2 (Aa --> Ss)

• C. Triangle Inequality Theorem 3 ( S₁ + S₂ > S₃ )

• D. Exterior Angle Inequality Theorem 4

A theorem that states,” The measure of an exterior angle is greater than the measure of either of the remote interior angles”.

• Triangle Inequality Theorem 1 (Ss à Aa)

• Triangle Inequality Theorem 2 (Aa à Ss)

• Triangle Inequality Theorem 3 ( S₁ + S₂ > S₃ )

• Exterior Angle Inequality Theorem 4

If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second. What theorem is this?

• Converse of Hinge Theorem (SSS Inequality Theorem)

• Hinge Theorem (SAS Inequality Theorem)

• Triangle Inequality Theorem 3 ( S₁ + S₂ > S₃ )

• Exterior Angle Inequality Theorem 4

A theorem that states, “The sum of the lengths of any two sides of a triangle is greater than the length of the third side.”

• Hinge Theorem (SAS Inequality Theorem)

• Triangle Inequality Theorem 2 (Aa à Ss)

• Triangle Inequality Theorem 3 ( S₁ + S₂ > S₃ )

• Exterior Angle Inequality Theorem 4

If two sides of a triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle in the first triangle is greater than the included angle in the second triangle.

• Converse of Hinge Theorem (SSS Inequality Theorem)

• Hinge Theorem (SAS Inequality Theorem)

• Triangle Inequality Theorem 3 ( S₁ + S₂ > S₃ )

• Exterior Angle Inequality Theorem 4

In the figure above, a crane is shown lifting an object to two different heights. The length of the arm of the crane is fixed. Which is shorter side MN or side RS?

• MN

• RS

• None

The figure below represents a tent in the forest. In the figure, is it possible that the measure of angle BAD is equal to 50◦ given that

 the measure of angle B = 70◦ ? Why?

• Yes, because you can assign any measurement to an angle.

• No, because exterior angle is greater than the remote interior angle.

• Cannot be determined

If the two sides of a triangle are 2 and 7. Find all the possible lengths of the third side.

• -5 < x < 9

• 2 < x < 7

• 5 < x < 9

Two roads meet at an angle of 50◦ at point A. A third road from B to C makes ang angle of 45◦ with the road from A to C. Which intersection, A or B, is closer to C? Explain.

• Cannot be determined

• B, because the opposite side is longer than A. The longer, it is closer to C.

• A, because the opposite side is shorter than B. The shorter, it is closer to C.

• None, because B has no angle.

Replace each o with < , > , or = to make a true sentence

• >

• =

• <