Hachie Chapter 5

Question 1

Triangle MidsegmentTheorem

Answer 1

If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length.

Question 2

Perpendicular Bisector Theorem

Answer 2

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Question 3

Converse of the Perpendicular Bisector Theorem

Answer 3

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Question 4

Angle Bisector Theorem

Answer 4

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

Question 5

Converse of the Angle Bisector Theorem

Answer 5

If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

Question 6

The perpendicular bisectors of the sides of a triangle

Answer 6

are concurrent at a point equidistant from the vertices.

Question 7

The bisectors of the angles of a triangle

Answer 7

are concurrent at a point equidistant from the sides.

Question 8

The medians of a triangle

Answer 8

are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.

Question 9

The lines that contain the altitudes of a triangle

Answer 9

are concurrent.

Question 10

Corollary to the Triangle Exterior Angle Theorem

Answer 10

The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

Question 11

If two sides of a triangle are not congruent

Answer 11

then the larger angle lies opposite the longer side

Question 12

If two angles of a triangle are not congruent,

Answer 12

then the longer side lies opposite the larger angle

Question 13

Triangle Inequality Theorem

Answer 13

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