Geometry Theorems

Question 1

Triangle Sum Theorem

Answer 1

The sum of the measures of the interior angles is 180 degrees.

Question 2

Exterior Angle Theorem

Answer 2

The measure of an exterior angle is equal to the sum of the measures of its two nonadjacent interior angles

Question 3

3rd Angles Theorem

Answer 3

If two angles of 1 triangle are congruent to two angles of another, then the 3rd angle is also congruent

Question 4

AAS Congruence Theorem

Answer 4

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent

Question 5

Base Angles Theorem

Answer 5

If two sides of a triangle are congruent, then the sides opposite them are congruent

Question 6

Perpendicular Bisector Theorem

Answer 6

If a point is on the perpendicular bisector of a segment, then it is equidistant from the end points of the segment

Question 7

Perpendicular Bisector Converse Theorem

Answer 7

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

Question 8

Angle Bisector Theorem

Answer 8

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

Question 9

Angle Bisector Converse Theorem

Answer 9

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

Question 10

Mid Segment Theorem

Answer 10

The segments connecting the midpoints of two sides of a triangle is parallel to the third side and half of the third side

Question 11

Triangle Inequality

Answer 11

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

Question 12

SSS Similarity Theorem

Answer 12

If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar

Question 13

SAS Similarity Theorem

Answer 13

If an angle of one triangle is congruent to an angle of a second triangle and the length of the sides including these angles are proportional , then the triangles are similar

Question 14

Triangle Proportionality Theorem

Answer 14

If a line is parallel to one side of triangle and intersects the other two sides, then it divides the two sides proportionally

Question 15

Equal Products Theorem: Intersecting Secants

Answer 15

If two secants intersect outside a circle, the product of the lengths of one of the secants and its external segment equals the product of the lengths of the other secant and its external segment

Question 16

Equal Products Theorem: Corresponding Angle Bisectors

Answer 16

Corresponding angle bisectors of two SIMILAR triangles have the same ratio as a pair of corresponding sides

Question 17

Equal Products Theorem: Corresponding Medians

Answer 17

Corresponding medians of two SIMILAR triangles have the same ratio as a pair of corresponding sides

Question 18

Equal Products Theorem: Intersecting Chords

Answer 18

If two chords intersect within a circle, the product of the lengths of the segments of 1 chord equals the product lengths of the segments of the other

Question 19

Converse of Corresponding Angles Theorem

Answer 19

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel

Question 20

Congruence Supplements Theorem

Answer 20

If 2 angles are complementary to the same angle, then they are congruent to each other

Question 21

Relfexive Property

Answer 21

For any number (or segment, angle, shape, et al), it has to be equal to to itself

Question 22

Transitive Property

Answer 22

If two geometric objects are congruent to a third geometric object, then they are congruent to each other