Geometry Midterm Info.

Front 1

Theorem 1-1

Back 1

if two lines intersect, then they intersect in exactly one point

Front 2

Theorem 1-2

Back 2

Through a line and a point not in the line there is exactly one plane

Front 3

Theorem 1-3

Back 3

If two lines intersect, then exactly one plane contains the lines

Front 4

Theorem 2-1 (Midpoint Theorem)

Back 4

If M is the midpoint of (segment) AB, then AM=1/2AB and MB=1/2AB

Front 5

Theorem 2-2 (Angle Bisector Theorem)

Back 5

if (ray) BX is the bisector of angle ABC, then m(angle)ABX=1/2 m(angle)ABC and m(angle)XBC=1/2 m(angle)ABC

Front 6

Theorem 2-3

Back 6

Vertical angles are congruent

Front 7

Theorem 2-4

Back 7

If two lines are perpendicular, then they form congruent adjacent angles

Front 8

Theorem 2-5

Back 8

If two lines form congruent adjacent angles, then the lines are perpendicular

Front 9

Theorem 2-6

Back 9

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary

Front 10

Theorem 2-7

Back 10

If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent

Front 11

Theorem 2-8

Back 11

If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent

Front 12

Theorem 3-1

Back 12

If two parallel planes are cut by a third plane, then the lines of intersection are parallel

Front 13

Theorem 3-2

Back 13

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

Front 14

Theorem 3-3

Back 14

If two parallel lines are cut by a tranversal, then same-side interior angles are supplementary

Front 15

Theorem 3-4

Back 15

if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also

Front 16

Theorem 3-5

Back 16

If two lines are cut by the transversal and alternate interior angles are congruent, then the lines are parallel

Front 17

Theorem 3-6

Back 17

If two lines are cut by a transversal and same-side interior angles are supplementary , then and lines are parallel

Front 18

Theorem 3-7

Back 18

In a plane two lines perpendicular to the same line are parallel

Front 19

Theorem 3-8

Back 19

Through a point outside a line, there is exactly one line parallel to the given line

Front 20

Theorem 3-9

Back 20

Through a point outside a line, there is exactly one line perpendicular to the given line

Front 21

Theorem 3-10

Back 21

two lines parallel to a third line are parallel to each other

Front 22

Theorem 3-11

Back 22

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

Front 23

Theorem 3-11 Corollary 1

Back 23

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

Front 24

Theorem 3-11 Corollary 2

Back 24

Each angle of an equiangular triangle has measure 60

Front 25

Theorem 3-11 Corollary 3

Back 25

In a triangle, there can be at most one right angle or obtuse angle

Front 26

Theorem 3-11 Corollary 4

Back 26

The acute angles of a right triangle are complementary

Front 27

Theorem 3-12

Back 27

The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles

Front 28

Theorem 3-13

Back 28

The sum of the measures of the angles of a convex polygon with n sides is (n-2)180

Front 29

Theorem 3-14

Back 29

The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex is 360

Front 30

Theorem 4-1 (Isosceles Triangle Theorem)

Back 30

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

Front 31

Theorem 4-1 Corollary 1

Back 31

An equilateral triangle is also equiangular

Front 32

Theorem 4-1 Corollary 2

Back 32

An equilateral triangle has three 60 degree angles

Front 33

Theorem 4-1 Corollary 3

Back 33

The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint

Front 34

Theorem 4-2

Back 34

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

Front 35

Theorem 4-2 Corollary 1

Back 35

An equiangular triangle is also equilateral

Front 36

Theorem 4-3 (AAS Theorem)

Back 36

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

Front 37

Theorem 4-4 (HL Theorem)

Back 37

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent

Front 38

Theorem 4-5

Back 38

If a point lies on the perpendicular bisector of a segment, then the point is equidistant for the endpoints of the segment

Front 39

Theorem 4-6

Back 39

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

Front 40

Theorem 4-7

Back 40

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

Front 41

Theorem 4-8

Back 41

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

Front 42

Theorem 5-1

Back 42

Opposite sides of a parallelogram are congruent

Front 43

Theorem 5-2

Back 43

Opposite angles of a parallelogram are congruent

Front 44

Theorem 5-3

Back 44

Diagonals of a parallelogram bisect each other

Front 45

Theorem 5-4

Back 45

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Front 46

Theorem 5-5

Back 46

If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram

Front 47

Theorem 5-6

Back 47

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallogram

Front 48

Theorem 5-7

Back 48

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

Front 49

Theorem 5-8

Back 49

if two lines are parallel, then all points on one line are equidistant from the other line

Front 50

Theorem 5-9

Back 50

If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

Front 51

Theorem 5-10

Back 51

a line that contains the midpoint of one side of a triangle and is parallel to another side passes through the midpoint of the third side

Front 52

Theorem 5-11

Back 52

The segment that joins the midpoints of two sides of a triangle
(1) is parallel to the third side
(2) is half as long as the third side

Front 53

Theorem 5-12

Back 53

Diagonals of a rectangle are congruent

Front 54

Theorem 5-13

Back 54

The diagonals of a rhombus are perpendicular

Front 55

Theorem 5-14

Back 55

Each diagonal of a rhombus bisects two angles of the rhombus

Front 56

Theorem 5-15

Back 56

The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices

Front 57

Theorem 5-16

Back 57

If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle

Front 58

Theorem 5-17

Back 58

If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus

Front 59

Theorem 5-18

Back 59

Base angles of an isosceles trapezoid are congruent

Front 60

Theorem 5-19

Back 60

The median of a trapezoid
(1) is parallel to the bases
(2) has a length equal to the average of the base lengths.