theorems page 2

Question 1

reflections in intersecting Lines theorem

Answer 1

if lines K and M intersect at point P, then a reflection in-line K followed by a reflection in line M is the same as a rotation about. P. The angle of rotation is 2X , where X is the measure of the acute or right angle formed by lines K and M

Question 2

triangle sum theorem

Answer 2

The sum of the measures of the interior angles of a triangle is 180

Question 3

exterior angle theorem

Answer 3

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

Question 4

corollary to the triangle sum theorem

Answer 4

The acute angles of a right triangle are complementary

Question 5

third angles theorem

Answer 5

if two angles of one triangle are congruent to two angles of another triangle then the third angles are also congruent

Question 6

Side – angle – side congruence theorem

Answer 6

if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle then the two triangles are congruent

Question 7

bass angles theorem

Answer 7

if two sides of a triangle are congruent then the angles opposite of them are congruent

Question 8

Converse of the base angles theorem

Answer 8

if two angles of a triangle are congruent then the sides opposite them are congruent

Question 9

corollary to the base angles theorem

Answer 9

if a triangle is equal lateral then it is equiangular

Question 10

corollary to the converse of the base angles theorem

Answer 10

if a triangle is equiangular then it is equal lateral

Question 11

Side – side – side congruence theorem

Answer 11

if three sides of one triangle are congruent to three sides of the second triangle then the two triangles are congruent

Question 12

hypotenuse – leg congruence theorem

Answer 12

if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle then the two triangles are congruent

Question 13

angle – Side – angle congruence theorem

Answer 13

if two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle then the two triangles are congruent

Question 14

angle – angle – side congruence theorem

Answer 14

if two angles and did not included Side of one triangle are congruent to two angles any corresponding non-included side of the second triangle then the two triangles are congruent

Question 15

perpendicular bisector theorem

Answer 15

any point if a point lies on the perpendicular bisector of a segment then it is equidistant from the endpoints of the segment

Question 16

Converse of the perpendicular bisector theorem

Answer 16

in a plane, if a point is equidistant from the endpoints of a segment then it lies on the perpendicular bisector of the segment

Question 17

angle bisector theorem

Answer 17

if a point lies on the bisector of an angle that it is equidistant from the two sides of an angle

Question 18

Converse of the angle by sector theorem

Answer 18

if a point is in the interior I’ve been angle and is equidistant from the two sides of the angle that it lies on the bisector of the angle

Question 19

circumcenter theorem

Answer 19

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

Question 20

in center theorem

Answer 20

The in center of a triangle is equidistant from the sides of the triangle

Question 21

centroid theorem

Answer 21

The centroid of a triangle is two thirds the distance from each vertex to the midpoint of the opposite side