Unit 6
Point of concurrency and Property of:
Perpendicular Bisector
Angle Bisector
Perpendicular Bisector: Circumcenter, equidistant to the three vertices of the triangle.
Angle Bisector: Incenter, equidistant to the three sides of the triangle.
Pythagorean Theorem
In a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse (a2+b2=c2).
Definition of a Polygon
A plane figure (2-d) that is formed by 3 or more segments called sides.
Radius: segment from center to point on the circle
Chord: segment whose endpoints are on the circle
Diameter: chord that passes through the center
Secant: line that passes through two points on the circle
Tangent: line that intersects the circle at one point (point of tangency)
What are the 4 types of transformations
Translation, Rotation, Dilation, and Reflection
Bonus: Tessellation
Point of concurrency and property of:
Median and Altitude
Median: Centroid, divides each median into segments in a 2:1 ratio.
Altitude: Orthocenter
Pythagorean Triples
3,4,5 / 5,12,13 / 8,15,17
Definition of Regular Polygon
Both equilateral and equiangular
Circumference and area of a circle formula
Circumference: πd or 2πr
Area: πr2
Definition of Translation
A figure slides to a new location
Largest side is opposite the largest angle.
Smallest side is opposite the smallest angle.
45o-45o-90o Theorem
In a 45o-45o-90o right triangle, if the legs have length x, then the hypotenuse has length x√2
If a quadrilateral is a parallelogram, then...
-Its opposite sides are congruent.
-Its opposite angles are congruent.
-Its consecutive angles are supplementary.
-Its diagonals bisect each other.
Equation of a circle
(x-h)2+(y-k)2=r2
Definition of Reflection
A figure is flipped over a line that acts a mirror.
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
300-60o-90o Theorem
In a 300-60o-90o right triangle, if the short leg has length x, then the long leg has length x√3 and the hypotenuse has length 2x.
What are the special quadrilaterals
Rhombus, Rectangle, Square, Trapezoid, and Kite
Surface Area and Volume formulas
SA= 2B+Ph
V=Bh
For Pyramid and Cone:
SA=B+1/2 Ps
V=1/3 Bh
Definition of Rotation and Dilation
Rotation: A figure is turned about a point.
Dilation: A figure is enlarged or reduced. NOT AN ISOMETRY!
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
SOH-CAH-TOA
SOH- Sineθ = Opposite/Hypotenuse
CAH- Cosineθ = Adjacent/Hypotenuse
TOA- Tangentθ = Opposite/Adjacent
Perimeter and Area formulas
Perimeter:
Rectangle= 2L+2WTriangle= a+b+c
Area:
Rectangle and Square= L*W or b*h
Triangle= 1/2 b*h
Parallelogram= b*h
Rhombus= b*h (1/2 diagonal1 + diagonal2)
Trapezoid= 1/2 (base1+base2)*height
Kite: 1/2 diagonal1 * diagonal2
Similar Solids: Scale factor, Surface Area ratio, and Volume Ratio
Scale factor= a:b
Surface Area ratio= a2:b2
Volume ratio= a3:b3
A tiling, or arrangement of closed shapes that completely covers the plane without overlapping and without leaving gaps.