Postulates & Theorems - chapter 5

Question 1

PERPENDICULAR BISECTOR THEOREM: If a point is on the perpendicular bisector of a segment, then it is ….

Answer 1

equidistant from the endpoints of the segment. (theo. 5-1-1)

Question 2

CONVERSE OF THE PERPENDICULAR BISECTOR THEOREM: If a point is equidistant from the endpoints of a segment, then ….

Answer 2

it is on the perpendicular bisector of the segment. (theo. 5-1-2)

Question 3

ANGLE BISECTOR THEOREM: If a point is on the bisector of an angle, then ….

Answer 3

it is equidistant from the sides of the angle. (theo. 5-1-3)

Question 4

CONVERSE OF THE ANGLE BISECTOR THEOREM: If a point in the interior of an angle is equidistant from the sides of the angle, then ….

Answer 4

it is on the bisector of the angle. (theo. 5-1-4)

Question 5

CIRCUMCENTER THEOREM: The circumcenter of a triangle is equidistant from ….

Answer 5

the vertices of the triangle. (theo. 5-2-1)

Question 6

INCENTER THEOREM: The incenter of a triangle is equidistant from ….

Answer 6

the sides of the triangle. (theo. 5-2-2)

Question 7

CENTROID THEOREM: The centroid of a triangle is located 2/3 of the distance ….

Answer 7

from each vertex to the midpoint of the opposite side. (theo. 5-3-1)

Question 8

TRIANGLE MIDSEGMENT THEOREM: A midsegment of a triangle is ….

Answer 8

parallel to a side of the triangle, and its length is half the length of that side. (theo. 5-4-1)

Question 9

If 2 sides of a triangle are not congruent, then the larger angle ….

Answer 9

is opposite the longer side. (theo. 5-5-1)

Question 10

If 2 angles of a triangle are not congruent, then the longer side ….

Answer 10

is opposite the larger angle. (theo. 5-5-2)

Question 11

TRIANGLE INEQUALITY THEOREM: The sum of any 2 side lengths of a triangle is ….

Answer 11

greater than the third side length. (theo. 5-5-3)

Question 12

HINGE THEOREM: If 2 sides of one triangle are congruent to 2 sides of another triangle and the included angles are not congruent, then ….

Answer 12

the longer third side is across from the larger included angle. (theo. 5-6-1)

Question 13

CONVERSE OF THE HINGE THEOREM: If 2 sides of one triangle are congruent to 2 sides of another triangle and the third sides are not congruent, then ….

Answer 13

the larger included angle is across from the longer third side. (theo, 5-6-2)

Question 14

CONVERSE OF THE PYTHAGOREAN THEOREM: If the sum of the squares of the lengths of 2 sides of a triangle is equal to the square of the length of the third side, then ….

Answer 14

the triangle is a right triangle. (theo. 5-7-1)

Question 15

PYTHAGOREAN INEQUALITIES THEOREM: In triangle ABC, c is the length of the longest side. If c^2 > a^2 + b^2, then …. (a), and if c^2 < a^2 + b^2, then …. (b)

Answer 15

(a) triangle ABC is an obtuse triangle

b) triangle ABC is an acute triangle. (theo. 5-7-2

Question 16

45-45-90 DEGREE TRIANGLE THEOREM: In a 45-45-90 degree triangle, both legs are …. (a), and the length of the hypotenuse is ….

Answer 16

(a) congruent

b) the length of a leg times square root of 2. (theo. 5-8-1

Question 17

30-60-90 DEGREE TRIANGLE THEOREM: In a 30-60-90 degree triangle, the length of the hypotenuse is …. (a), and the length of the longer leg is …. (b)

Answer 17

(a) 2 times the length of the shorter leg.

b) the length of the shorter leg times square root of 3. (theo. 5-8-2