6 Flashcards
(26 cards)
Theorem: Diagonal of a Parallelogram Creates Congruent Triangles
What it is: The diagonal of a parallelogram divides it into two congruent triangles.
Converse: If a quadrilateral’s diagonal divides it into two congruent triangles, then it is a parallelogram.
Theorem: Opposite Sides and Angles of a Parallelogram
What it is: If a quadrilateral is a parallelogram, then it has congruent opposite sides and angles.
Converse: If a quadrilateral has congruent opposite sides and angles, then it is a parallelogram.
Theorem: Congruent Opposite Sides → Parallelogram
What it is: If a quadrilateral has congruent opposite sides, then it is a parallelogram.
Converse: If a quadrilateral is a parallelogram, then it has congruent opposite sides.
Theorem: Congruent Opposite Angles → Parallelogram
What it is: If a quadrilateral has congruent opposite angles, then it is a parallelogram.
Converse: If a quadrilateral is a parallelogram, then it has congruent opposite angles.
Theorem: Polygon Angle Sum Theorem
What it is: The sum of the interior angles of an n-sided polygon is 180(n-2).
Example: For a hexagon (n=6), the sum of the interior angles is 180(6-2) = 720°.
Theorem: Measure of an Interior Angle in a Regular Polygon
What it is: The measure of an interior angle in a regular polygon is [180(n-2)]/n.
Example: In a regular hexagon, each interior angle is [180(6-2)]/6 = 120°.
Theorem: Two Pairs of Opposite Congruent Sides → Parallelogram
What it is: If a quadrilateral has two pairs of opposite congruent sides, then it is a parallelogram.
Converse: If a quadrilateral is a parallelogram, then it has two pairs of opposite congruent sides.
Theorem: Diagonals Bisect Each Other in a Parallelogram
What it is: If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Converse: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Theorem: One Pair of Congruent and Parallel Sides → Parallelogram
What it is: If a quadrilateral has one pair of congruent and parallel sides, then it is a parallelogram.
Converse: If a quadrilateral is a parallelogram, then it has one pair of congruent and parallel sides.
Theorem: Rectangle Properties
What it is: A rectangle is a parallelogram, and all its angles are congruent (right angles).
Example: A square is a rectangle because it has four right angles.
Theorem: Rectangle’s Diagonals are Congruent
What it is: If a quadrilateral is a rectangle, then its diagonals are congruent.
Converse: If a parallelogram has congruent diagonals, then it is a rectangle.
Theorem: Right Angle → Rectangle
What it is: If a parallelogram has a right angle, then it is a rectangle.
Example: A square is a rectangle because all its angles are right angles.
Theorem: Rhombus Properties
What it is: A rhombus is a parallelogram, and its diagonals are perpendicular.
Converse: If a quadrilateral has perpendicular diagonals, then it is a rhombus.
Theorem: Rhombus Diagonals Bisect Opposite Angles
What it is: If a quadrilateral is a rhombus, then its diagonals bisect opposite angles.
Converse: If a quadrilateral’s diagonals bisect opposite angles, then it is a rhombus.
Theorem: Square Properties
What it is: A square is a rectangle, parallelogram, and rhombus.
Example: A square has all the properties of a rectangle (right angles) and a rhombus (congruent sides).
Theorem: Isosceles Trapezoid Properties
What it is: If a trapezoid is isosceles, then it has two pairs of congruent base angles.
Converse: If a trapezoid has two pairs of congruent base angles, then it is isosceles.
Theorem: Isosceles Trapezoid Diagonals
What it is: If a trapezoid is isosceles, then its diagonals are congruent.
Converse: If a trapezoid has congruent diagonals, then it is isosceles.
Theorem: Kite Properties
What it is: If a quadrilateral is a kite, then its diagonals are perpendicular.
Converse: If a quadrilateral has perpendicular diagonals, then it is a kite.
Theorem: Kite Diagonals Bisect Opposite Angles
What it is: If a quadrilateral is a kite, then one diagonal bisects the other and one diagonal bisects a pair of opposite angles.
Converse: If one diagonal bisects a pair of opposite angles, then the quadrilateral is a kite.
Theorem: Rhombus if Four Congruent Sides
What it is: A quadrilateral is a rhombus if it has four congruent sides.
Example: A square is a rhombus because it has four congruent sides.
Theorem: Trapezoid Properties
What it is: A quadrilateral is a trapezoid if it has exactly one pair of parallel sides.
Example: A parallelogram has two pairs of parallel sides, but a trapezoid has only one.
Theorem: Isosceles Trapezoid Legs
What it is: A trapezoid is isosceles if it has congruent legs.
Example: In an isosceles trapezoid, the non-parallel sides are congruent.
Theorem: Kite Properties
What it is: A quadrilateral is a kite if it has two pairs of consecutive congruent sides and opposite sides are not congruent.
Example: A diamond shape is a kite, with adjacent sides being equal.
Theorem: Equilateral Polygon
What it is: A polygon is equilateral if all its sides are congruent.
Example: An equilateral triangle has all three sides the same length.
