Geometry Review Flashcards

Flashcards for vocabulary review based on lecture notes about polygons, geometry proofs, and properties of quadrilaterals.

Polygon

A simple closed curve consisting solely of line segments.

Median of a polygon

A line segment drawn from a vertex to the midpoint of the opposite side.

Exterior angles of a polygon

The sum of all exterior angles is 360°.

Proving Parallelograms

Show: 1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite sides are parallel. 3. One pair of opposite sides are parallel and congruent. 4. Diagonals bisect each other. 5. Both pairs of opposite angles are congruent.

Proving Rectangles

Show: 1. It is a parallelogram with a right angle. 2. It is a parallelogram whose diagonals are congruent. 3. It is an equiangular quadrilateral (all angles congruent).

Proving Rhombuses

Show: 1. It is an equilateral quadrilateral. 2. It is a parallelogram with 2 consecutive sides that are congruent. 3. It is a parallelogram whose diagonals are perpendicular. 4. It is a parallelogram whose diagonals bisect its angles.

Proving Squares

Show: 1. It is a rectangle with 2 consecutive sides that are congruent. 2. It is a rhombus with 1 right angle.

Reflexive Property

Any segment or angle is congruent to itself (e.g., <A = <A).

Substitution Property

Any equality may be reversed; If a = b, then b = a.

Transitive Property

If quantities are equal to the same quantity, they are equal to each other; If a = b and c = b, then a = c.

Partition Postulate Property

A whole quantity is equal to the sum of its parts; AB + BC = AC.

Addition Postulate Property

If equal quantities are added to equal quantities, the sums are equal; If a = b and c = d, then a + c = b + d.

Subtraction Postulate Property

If equal quantities are subtracted from equal quantities, the differences are equal; If a = b and c = d, then a - c = b - d.

Parallelogram Properties

The opposite sides are parallel, the opposite sides are congruent, the opposite angles are congruent, the diagonals bisect each other, any pair of consecutive angles are supplementary, and diagonals form 2 congruent triangles.

Rectangle Properties

All the properties of a parallelogram apply, all angles are right angles, and the diagonals are congruent.

Kite Properties

Two disjoint pairs of consecutive sides are congruent, the diagonals are perpendicular, one diagonal is the perpendicular bisector of the other, one of the diagonals bisects a pair of opposite angles, and one pair of opposite angles are congruent.

Rhombus Properties

All the properties of a parallelogram apply, two consecutive sides are congruent, all sides are congruent, the diagonals bisect the angles, the diagonals are perpendicular bisectors of each other, and the diagonals divide the rhombus into four congruent right triangles.

Square Properties

All the properties of a rectangle apply, all the properties of a rhombus apply, the diagonals form four isosceles right triangles, and adjacent sides are perpendicular.

Isosceles Trapezoid Properties

The legs are congruent, the bases are parallel, the lower base angles are congruent, the upper base angles are congruent, the diagonals are congruent, and any lower base angle is supplementary to any upper base angle.