# Geometry

## 30 terms

### parallelogram

a quadrilateral is a parallelogram iff both pairs of opposite sides are parallel

### rectangle

a parallelogram is a rectangle iff it has one right angle

### rhombus

a parallelogram is a rhombus iff two consecutive sides are congruent

### square

a parallelogram is a square iff it is both a rectangle and a rhombus

### kite

a quadrilateral is a kite iff two disjoint pairs of sides are congruent

### trapezoid

a quadrilateral is a trapezoid iff exactly one pair of opposite sides are parallel

### isosceles trapezoid

a trapezoid is isosceles iff the legs are congruent

### parallelogram theorem

if a quadrilateral is a parallelogram, then opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, diagonals bisect each other

### rectangle diagonal theorem

a parallelogram is a rectangle iff diagonals are congruent

### kite diagonal theorem

a quadrilateral is a kite iff one diagonal is the perpendicular bisector of the other, perpendicular bisector also bisects the vertex angles

### rhombus diagonal theorem

a parallelogram is a rhombus iff diagonals bisect vertex angles, a quadrilateral is a rhombus iff diagonals are the perpendicular bisectors of each other

### isosceles trapezoid theorem

a trapezoid is isosceles iff a pair of base angles is congruent

### isosceles trapezoid diagonal theorem

a trapezoid is isosceles iff diagonals are congruent

### 5-way theorem

a quadrilateral is a parallelogram if one of the following five things is true: 1. both pairs of opposite sides are parallel 2. both pairs of opposite sides are congruent 3. one pair of opposite sides is both congruent and parallel 4. the diagonals bisect each other 5. both pairs of opposite angles are congruent

### definition of a line perpendicular to a plane

if a line is perpendicular to a plane, then the line is perpendicular to every line in the plane passing through the foot

### perpendicular line plane theorem

if a line is perpendicular to two distinct lines contained in a plane, then the line is perpendicular to the plane

### definition of parallel planes

two planes are parallel iff they do not intersect

### parallel plane intersection theorem

if a plane intersects two parallel planes, then the lines of intersection are parallel

### 5 statements - parallelism

1. two planes perpendicular to the same line are parallel 2. if a line is perpendicular to one of the two parallel planes, it's perpendicular to the other 3. if two planes are both parallel to a third plane, then the first two planes are parallel to each other 4. two planes perpendicular to the same plane in distinct lines are parallel to each other 5. if a plane is perpendicular to one of two parallel lines, then it is perpendicular to the other

### triangle sum theorem

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

### remote exterior angle theorem

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

### midsegment/midline (triangle) definition

a midsegment of a triangle has endpoints that are midpoints of two sides and is parallel to the remaining side

### midsegment theorem

if a segment is a midsegment of a triangle, then its length is one-half of the side to which it is parallel

### no choice theorem

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

### regular polygon definition

a polygon is regular iff it is equiangular and equilateral

(n-2)(180)

[(n-2)(180)]/n

360

360/n

[n(n-3)]/2