Postulates and Theorems

Question 1

Segment Addition Postulate

Answer 1

If B is a point on line AC, then AB + BC = AC.

Question 2

Angle Addition Postulate

Answer 2

If point R is in the interior of angle QPS, then the measurement of angle QPR + the measurement of angle RPS is equal to the measurement of angle QPS.

Question 3

Corresponding Angles Postulate

Answer 3

If two parallel lines are cut by a transversal, their corresponding angles are congruent.

Question 4

Alternate Interior Angles Theorem

Answer 4

If two parallel lines are cut by a transversal, then their alternate interior angles are congruent.

Question 5

Alternate Exterior Angles Theorem

Answer 5

If two parallel lines are cut by a trasnversal, then their alternate exterior angles are congruent.

Question 6

Same-side Interior Angles Theorem

Answer 6

When two parallel lines are intersected by a transversal, then their same-side interior angles are suppplementary.

Question 7

Isoceles Triangle Theorem

Answer 7

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

The converse of this is also true.

Question 8

Side-Side-Side (SSS) Congruence Postulate

Answer 8

If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.

Question 9

Side-Angle-Side (SAS) Congruence Postulate

Answer 9

If two sides and the included angle of one triangle are congruent to two corresponding sides and the included angle of another triangle, then the triangles are congruent.

Question 10

Angle-Side-Angle (ASA) Congruence Postulate

Answer 10

If two angles and the included side of one triangle are congruent to two corresponding angles and the included side of another triangle, then the triangles are congruent.

Question 11

Angle-Angle-Side (AAS) Congruence Theorem

Answer 11

If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.

Question 12

Hypotenuse-Leg (HL) Theorem

Answer 12

Specifically for right triangles, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and the corresponding leg of another right triangle, then the triangles are congruent.

Question 13

Perpendicular Bisector Theorem

Answer 13

If a point is on the perpendicular bisector of a line segment, then the point is equidistant to the segment’s enpoints.

The converse of this is also true.

Question 14

Circumcenter Theorem

Answer 14

The circumcenter of a triangle is equidistant to all the vertices.

Question 15

Incenter Theorem

Answer 15

The incenter is equidistant to all the sides of the triangle.

Question 16

Centroid Theorem

Answer 16

The centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.

Question 17

Triangle Inequality Theorem

Answer 17

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

Question 18

Opposite Sides Theorem

Answer 18

If both pairs of opposite sides are congruent, then it is a paralellogram.

Question 19

Opposite Angle Theorem

Answer 19

If both pairs of opposite angles are congruent, then it is a paralellogram.

Question 20

Consecutive Angles Theorem

Answer 20

If an angle is supplementary to both of its consecutive angles, then it is a parallelogram.

Question 21

Diagonal Bisector Theorem

Answer 21

If a quadrilateral has diagonals that bisect each other, then it is a parallelogram.

Question 22

One Pair of Opposite Sides Theorem

Answer 22

If a quadrilateral has one pair of sides that is both congruent and parallel, then it is a parallelogram.