Download Geometry Review Morgan Parsons

Geometry Review
Morgan Parsons
Honors Geometry
Mrs. Lowe
June 2, 2009

Formulas:
Rectangle
Square
P = 2L + 2w
A= Lw
A= S²
P = 4s
w
L
Triangle
P=a+b+c a
A = ½ bh
b
Circle
C=2 r
A = r²
c
Tips for Next years students: know your formulas! Knowing
the formulas makes things easier as your geometry gets harder.
-Parallel lines are two lines that are coplanar and do not intersect.
-Perpendicular lines are two lines that intersect to form a right
angle
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs
of corresponding angles are congruent.
1
2
Example:
1  2
Two figures are congruent if they have exactly the same size and shape.
SSS Congruence Postulate – If 3 sides
of one triangle are congruent to the
three sides of a second triangle, then
the two triangles are congruent.
ASA Congruence Postulate – If 2 angles &
the included side of one triangle are
congruent to 2 angles & the included side of
a second triangle, then the 2 triangles are
congruent.
SAS Congruence Postulate – If 2 sides
and the included angle of one triangle
are congruent to two sides and the
included angle of a second triangle,
then the two triangles are congruent.
AAS Congruence Theorem – If 2 angles & a
non-included side of one triangle are
congruent to 2 angles & the corresponding
non-included side of a second triangle, then
the two triangles are congruent.
Chapter 6
Theorem 6.1 Interior Angles of a Quadrilateral
2
1
The sum of the measures of the interior angles of a
quadrilateral is 360
m1 + m2 + m3 + m4 = 360
4
3
Corollaries About Special Quadrilaterals
Rhombus Corollary
A quadrilateral is a rhombus if and only if it has four congruent sides.
Rectangle Corollary
A quadrilateral is a rectangle if and only if it has four right angles.
Square Corollary
A quadrilateral is a square if and only if it is a rhombus and a rectangle.
Chapter 7
Reflection – Where the line acts like a mirros, with an
image reflected in the line.
P’
Rotation – Transformation in which a figure is turned
around a fixed point.
Translation - a transformation that maps every two
points P and Q in the plane to points P’ and Q’, so that
the following properties are true.
1. PP’ = QQ’
2. PP’ || QQ’, or PP’ and QQ’ are collinear.
Q’
P
Q
Chapter 8
When there is a correspondence between two polygons such that their
corresponding angles are congruent and the lengths of corresponding
sides are proportional the two polygons are called similar polygons.
AA Similarity Postulate
If two angles of one triangle are congruent to
two angles of another triangle, then the two
triangles are similar.
SSS Similarity Theorem
If the lengths of the corresponding sides of two triangles
are proportional, then the triangles are similar.
SAS Similarity Theorem
If an angle of one triangle is congruent to an angle of a
second triangle and the lengths of the sides are
proportional then the triangles are similar.
Chapter 9
Right triangles whose angle measures are 45 -45 -90 or 30 -60 -90 are called
special right triangles.
45
45-45-90 Triangle Theorem
2x
x
In a 45-45-90 triangle, the hypotenuse is 2 times as long as each leg.
45
x
Hypotenuse = 2  leg
30-60-90 Triangle Theorem
In a 30-60-90 triangle, the hypotenuse is twice as long as the
shorter leg, and the longer leg is 3 times as the shorter leg.
60
x
2x
30
3x
Hypotenuse = 2  shorter leg
Longer leg =3  shorter leg
Chapter 10
Radius
Diameter
Center
Chapter 11
Circumference of a circle = 2r
Arc Length Corollary
In a circle, the ratio of the length of a given
arc to the circumference is equal to the ratio
of the measure of the arc to 360
Arc length of AB
2r
=
mAB
360
Area of a Sector
The ratio of the area A of a sector of a circle
to the area of a circle is equal to the ratio of
the measure of the intercepted arc to 360
Area of a circle = r2
A
r 2
=
mAB
360
Chapter 12
Volume Postulates
Postulate 27 Volume of a cube
The volume of a cube is the cube of the length of its side, or v = s³
Postulate 28 Volume Congruence Postulate
If two polyhedra are congruent, then they have the same volume.
Postulate 29 Volume Addition Postulate
The volume of a solid is the sum of the volumes of all its non-overlapping
parts.
Euler’s Theorem
The number of faces (F), vertices (V), and edged (E) of a polyhedron are related by
the formula F + V = E = 2.
:)
THE
END