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Geometry: Theorems

Problems

Basic Theorems for Triangles

Theorems for Segments within Triangles

Problem : Is it possible for the lengths of the sides of a triangle to be 1, 2, and 3? Why or why not?

No. 1 + 2 = 3 . The triangle inequality states that the sum of the lengths any two sides of a triangle must exceed the length of the third side.

Problem : Which side of the triangle below is the longest?

Side AC is the longest.

Problem : In triangle ABC, if side AB = 3, side BC = 4, and side CA = 5, which angle, A, B, or C, is the smallest?

Angle C

Problem : Is it possible for an exterior angle of a triangle to be smaller that one of the interior angles of the triangle?

Yes, the exterior angle must be acute, and the interior angle that is greater than the exterior angle must be adjacent (and therefore supplementary) to it. Only when the interior angle is obtuse is the exterior angle of a triangle smaller than that interior angle.

Problem : If an exterior angle of a triangle is 95 degrees, and one of the remote interior angles is 50 degrees, what is the measure of the other remote interior angle?

45 degrees

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