Relationships Within Triangles

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

If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.

• Perpendicular Bisector Theorem

• Angle Bisector Theorem

• Hinge Theorem

• Altitude

Find BD 

• 65

• 14

• 11

• 4

In a triangle, the three perpendicular bisectors are concurrent. The point of concurrency is the _____________ of the triangle.

• Circumcenter

• Incenter

• Median

• Centroid

The circumcenter of a triangle is equidistant from the vertices of the triangle.

• Centroid Theorem

• Circumcenter Theorem

• Perpendicular Bisector Theorem

• Hinge Theorem

The incenter of a triangle is equidistant from the ________ of the triangle.

• Sides

• Center

• Vertices

Find the coordinates of the circumcenter of the triangle with the given vertices.

• (1,5)

• (3,6)

• (2,3)

• (5,4)

A _______________ of a triangle is a segment that connects the midpoints of two sides of the triangle.

• Median

• Bisector

• Midsegment

• Slope

The vertices of a triangle are A(-5,6) B(3, 8) and C(1,-4)  What are the vertices of the midsegment triangle?

• (1,- 7), (−2, 10), (2, 12)

• (−1, 7), (−2, 1), (2, 2)

• (−1, 14), (−2, 5), (4, 2)

• (−1, -7), (2, -1), (-2, 2)

If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

• Triangle Longer Side Theorem

•  Triangle Larger Angle Theorem

•  Triangle Smaller Angle Theorem

•  Triangle Shorter Side Theorem