Download PROPERTIES OF QUADRILATERALS

PROPERTIES OF QUADRILATERALS
Parallelograms:
1) Both pairs of opposite sides are congruent and parallel.
2) Both pairs of opposite angles are congruent.
3) One pair of opposite sides is both parallel and congruent.
4) The diagonals bisect each other.
Rectangles:
1) The diagonals are congruent.
2) Adjacent sides are perpendicular.
Rhombus:
1) Consecutive Sides are congruent.
2) One diagonal bisects the two opposite angles.
3) The diagonals are perpendicular.
Square:
1) That the quadrilateral is a rectangle.
2) That the quadrilateral is a rhombus.
Trapezoid:
1) Two and only two sides are parallel.
To prove a quadrilateral is an isosceles trapezoid
1) Congruent nonparallel sides.
2) Base angles congruent.
3) The diagonals are congruent.
Kite:
1) Two pairs of consecutive sides are congruent.
2) One of the diagonals is the perpendicular bisector of the other diagonal.
Fill in the chart using the following:
Isosceles trapezoids
Kites
Parallelograms
Quadrilaterals
Rectangles
Rhombuses
Squares
Trapezoids
(2)
(1)
(3)
(4)
(7)
(6)
(5)
(8)
Right Triangles
Special right triangles:
Trigonometry: SOH CAH TOA!!!
Remember: If you need the degree, use the inverse key!
Congruency Theorems
SAS
SSS
ASA
**CPCTC!
Remember: What two things can’t be in math?!
(RIGHT TRIANGLES ONLY!): HL, LA, LL
Similarity
AA
*SAS
*SSS
*There are different from the congruency theorems, for the sides only need
to be proportional to prove triangles similar
Using triangles/parts of a triangle
Pythagorean Theorem
Given two side lengths, find the range of the third length
Sum of two sides>last side
Triangle Angle Sum Theorem
Similar triangles (ratios!)
Geometric Mean
“Fork” theorems
h is the geometric mean of x and y
b is the geometric mean of x and x+y
a is the geometric mean of y and y+x
Circles
Central angle (=arc length) vs. inscribed angle (1/2 the length)
Radius and tangent are perpendicular
Quadrilateral inscribed in a circle-opposite angles are supplementary
Major arc (>180), minor arc (<180), semi circle (=180)
“Party Hat” theorem!
Arc length vs. Area of a sector vs. Area of a segment
Area and Volume
You should know these theorems! (we just did them ☺ )
Triangle, Rhombus, Kite, Trapezoid, Circle
Prism, Cylinder, Pyramid, Cone, sphere, “regular” shape