Quadrilateral and Polygon Unit Flashcards
Define parallelogram
A quadrilateral with both pair of opposite sides parallel
How do you name a parallelogram?
With the symbol for parallelogram and then all 4 vertices going around in a circle
What is the symbol for parallelogram?
A little parallelogram (▱)
Give the six properties for all parallelograms.
- Opposite sides are parallel
- Opposite sides are congruent
- Opposite angles are congruent
- Consecutive angles are supplementary
- Diagonals bisect each other
- Diagonal creates 2 congruent triangles
Give all the ways to prove a quadrilateral is a parallelogram.
- Both pairs of opposite sides are parallel
- Both pairs of opposite sides are congruent
- Both pairs of opposite angles are congruent
- All consecutive angles are supplementary
- The diagonals bisect each other
- One pair of opposite sides are congruent and parallel
Give the seven properties of any rhombus.
- All 4 sides are congruent
- Opposite sides are parallel
- Diagonals are angle bisectors
- Diagonals are perpendicular
- Diagonals bisect each other
- Opposite angles are congruent
- Consecutive angles are supplementary
Give the five properties of any rectangle.
- Opposite sides are congruent
- 4 right angles
- Diagonals are congruent
- Diagonals bisect each other
- Opposite sides are parallel
Give the seven properties of any square
- All 4 sides are congruent
- 4 right angles
- Diagonals are congruent
- Diagonals bisect each other
- Diagonals are angle bisectors (45º)
- Diagonals are perpendicular
- Opposite sides are parallel
Give the definition of a trapezoid.
A quadrilateral with only 1 pair of opposite sides parallel
What is the angle rule for trapezoids?
Same side interior angles are supplementary
What do we call the parallel sides of a trapezoid?
Bases
What do we call the nonparallel sides of a trapezoid?
Legs
Define a median of a trapezoid.
A line segment connecting the midpoint of the legs
What are the two properties for a median of a trapezoid?
- It’s parallel to the bases
- Its length is the average of the lengths of the bases
What makes a trapezoid isosceles?
The legs are congruent
Give the properties specific for an isosceles trapezoid.
- Legs are congruent
- Base angles are congruent
- Diagonals are congruent.
What are the two methods used to prove quadrilaterals congruent?
SASAS & ASASA
What is the key when naming 2 congruent quadrilaterals?
You must match up the corresponding parts / letters exactly.
Why is it important to match up the corresponding parts / letters exactly?
To be able to use CPCQC
If three or more parallel lines divide a transversal in to congruent segments, what else is true about those lines?
They are the same distance apart from each other.
What is true about any other transversal to those parallel lines?
It also divides that transversal in to congruent segments (it is an egg slicer).
What is the definition of polygon?
Many sided figure.
What are 3 things that make a figure not a polygon?
- No curves
- No overlapping sides
- It must be enclosed
What is the definition of concave polygon?
A polygon with at least one diagonal that goes outside the figure (A polygon with no ‘caved in’ or ‘dented in’ sides)
What is the definition of convex polygon?
A polygon that is not concave / A polygon with no diagonals that go outside the figure.
What is the definition of regular polygon?
A polygon with all sides congruent and all angles congruent.
Name the polygon with 7 sides.
Septagon or heptagon
Name the polygon with 10 sides.
Decagon
Name the polygon with 4 sides.
Quadrilateral
Name the polygon with 5 sides.
Pentagon
Name the polygon with 8 sides.
Octagon
Name the polygon with 15 sides.
15-gon
Name the polygon with 12 sides.
Dodecagon
Name the polygon with 6 sides.
Hexagon
Name the polygon with 50 sides.
50-gon
Name the polygon with 9 sides.
Nonagon
Name the polygon with 11 sides.
11-gon
Name the polygon with n sides.
n-gon
What is the formula for the sum of the measures of the interior angles for any convex polygon?
I = (n – 2) x 180°
What is the formula for the sum of the measures of the exterior angles for any convex polygon?
E = 360°
What is the formula for the measure of each interior angle of any regular polygon?
i = I / n = [(n – 2) x 180°] / n
What is the formula for the measure of each exterior angle of any regular polygon?
e = E / n = 360°/n
How do you find the measure of each interior angle of a polygon that is not regular?
You can not.
What is e + i ?
e + i = 180° (linear pair postulate)
How do you name a polygon?
Using all the vertices going around in a circle.
What is the symbol for polygon?
There is no symbol for polygon.
