TEST THURSDAY GEOMETRY Flashcards
Closed plane figure made up of line segments only joining at their endpoints *segments cannot be collinear
Regular Polygon (360/360 divided by n only applies to regular polygons!)
All interior angles are less than 180 degrees, no diagonals with points outside polygon
Convex Polygons
At least one interior angle greater than 180 degrees, reflexive angle present, at least one diagonal with points outside polygon
Concave Polygon
All sides and angles are congruent in a polygon
Regular polygon
triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, dodecagon
prefix polygons
The sum of the measures of the interior angles of the polygon with “n” sides, (n-2)180 (divide by n again to get individual angle measure)
Polygon Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon are always 360 degrees
Polygon Exterior Angle-Sum Theorem
Opposite sides are parallel & congruent, opposite angles are congruent and consecutive angles are supplementary. diagonals bisect each other.
classification of a parallelogram
All the properties of a parallelogram, four right angles, diagonals are congruent
classification of a rectangle
all properties of a parallelogram, rectangle, and rhombus
classification of a square
all properties of a parallelogram, all sides are congruent. The diagonals bisect the angles and are perpendicular
classification of a rhombus
at least one pair of parallel sides present
classification of a generalized trapezoid
non parallel lines are congruent, base angles are congruent, and opposite angles are supplementary
classification of an isosceles trapezoid
two pairs of adjacent sides are congruent, one pair of opposite angles are congruent, one diagonal bisects the other, and diagonals are perpendicular
classification of a kite
diagonals in a RECTANGLE are…
congruent
diagonals in a RHOMBUS are…
Perpendicular and bisect each other
What is the one generalization for all trapezoids?
At least ONE pair of parallel lines
Diagonals for a KITE are…
perpendicular and one diagonal bisects the other
how many pairs of adjacent sides are in a kite?
2 congruent pairs of adjacent sides
how many pairs of angles are in a kite and what type of angles are they?
One pair of OPPOSITE CONGUENT angles
Which parts are congruent in an isosceles trapezoid?
Non parallel sides and base angles are congruent in an isosceles trapezoid
Which angles are supplementary in an isosceles trapezoid?
opposite angles are supplementary in a trapezoid
What are the sides’ relationships with each other in a rhombus
all of the sides in a rhombus are congruent
what is the classification of the angles in a rectangle?
there are 4 right angles in a rectangle
what are the diagonals in a square?
the diagonals in a square bisect angles, are perpendicular & congruent
what are the properties of a square?
- consecutive angles are supplementary
- diagonals are congruent, bisect each other, and are perpendicular
- 4 right angles
- all sides are congruent
- opposite sides are parallel and congruent
- opposite angles are congruent
what are the properties of a rectangle?
- opposite sides are parallel and congruent
- opposite angles are congruent
- consecutive angles are supplementary
- diagonals bisect each other and are congruent
- 4 right angles
what are the properties of a rhombus?
- diagonals bisect each other. are angle bisectors, and are perpendicular
- all sides are congruent
- opposite parallel sides are congruent
- opposite angles are congruent
- consecutive angles are supplementary
what are the properties of a kite?
- 2 pairs of congruent adjacent sides
- one pair of opposite congruent angles
- one diagonal bisects the other and diagonals are perpendicular
what are the properties of a general trapezoid?
at least one pair of parallel lines
what are the properties of an isosceles trapezoid?
- at least one pair of parallel lines
- non parallel sides are congruent
- base angles are congruent
- opposite angles are supplementary
Theorems proving a quadrilateral is a parallelogram (includes special parallelograms)
- if both pairs of opposite sides are either congruent or parallelogram OR one pair of opposite sides are both congruent and parallel
- both pairs of opposite angles are congruent
- diagonals bisect each other
Proving rectangle theorems (when solving, using parallelogram theorems are a given)
- one right angle present
- diagonals are congruent
Proving rhombus with theorems (Using parallelogram theorems are a given)
- adjacent SIDES are congruent
- ## diagonals are perpendicular (and/or bisect angles)
Proving a square with theorems
Using criteria from both rhombus & rectangle (prove two of those criteria) ex. ABCD is a square because its diagonals are perpendicular and formed a right angle
Isosceles Trapezoid theorems (quadrilateral-trapezoid)
- base angles are congruent
- diagonals are congruent
Kite (Quadrilateral)
Diagonals are perpendicular
Quadrilateral Family Tree
Quadrilateral: Kite or Trapezoid: Isosceles Trapezoid or parallelogram: rectangle, square, rhombus
Construction for isosceles trapezoid
one pair of opposite sides are parallel
Construction for parallelogram
one pair of opposite sides are parallel and congruent
Construction for rectangle
both pairs of opposite sides are congruent and there is one right angle established
Construction for a hexagon
6 equilateral triangles are established
