Geometry Chapter 5 Theorems

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Theorem 5-3 (pg 167)

Diagonals of a parallelogram bisect each other

Theorem 5-17 (pg 185)

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

Theorem 5-18 (pg 190)

base angles of an isosceles trapezoid are congruent

Theorem 5-14 (pg 185)

each diagonal of a rhombus bisects two angles of the rhombus

Theorem 5-16 (pg 185)

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

Theorem 5-6 (pg 172)

if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 5-4 (pg 172)

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

Theorem 5-5 (pg 172)

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

Theorem 5-7 (pg 172)

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

Theorem 5-9 (pg 177)

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

Theorem 5-8 (pg 177)

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

Theorem 5-2 (pg 167)

opposite angles of a parallelogram are congruent

Theorem 5-1 (pg 167)

opposite sides of a parallelogram are congruent

Theorem 5-19 (pg 191)

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

Theorem 5-12 (pg 185)

The diagonals of a rectangle are congruent

Theorem 5-13 (pg 185)

The diagonals of a rhombus are perpendicular

Theorem 5-15 (pg 185)

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

Theorem 5-11 (pg 178)

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

Theorem 5-10 (pg 178)

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


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