Geometry Review Fall Semester
Supplementary angles
2 angles when added together that equal 180 degrees.They do not have to be adjacent angles.
Complementary angles
2 angles when added together that equal 90 degrees. They do not have to be adjacent angles.
Characteristics of Quadrilaterals
A parallelogram has two pairs of parallel sides; a trapezoid has exactly one pair of parallel sides; a rectangle is a parallelogram with four right angles; a rhombus is an equilateral parallelogram; a square is a rhombus with four right angles; a kite has two pairs of consecutive congruent sides.
The longest side of a triangle is opposite the largest angle
AB is the longest side because it is opposite largest angle. (100)
Area of a triangle
Base times the height divided by 2.
The point of concurrency of the three medians of a triangle is called the __________.
Centroid
The point of concurrency of the three perpendicular bisectors of a triangle is called the __________.
Circumcenter
CPCTC
Corresponding parts of Congruent Triangles are Congruent
HL Congruence Theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle.
SSS Congruence Theorem
If the three sides of one triangle are congruent to the three sides of another triangle.
AAS Congruence Theorem
If two angles and a non-included side of one triangle are congruent to two angles and a non- included angle of another triangle.
ASA Congruence Theorem
If two angles and an included side of one triangle are congruent to two angles and an included angle of another triangle.
SAS Congruence Theorem
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.
Parallel and perpendicular
Must know how to reach parallel and/or perpendicular from any given or determined slope.
SSA
NOT a valid congruency theorem.
The point of concurrency of the three altitudes of a triangle is called the __________.
Orthocenter
The Triangle Inequality Theorem
The sum of any two sides of a triangle MUST be larger than the third side. To check to see if three values would form a triangle, just add the two smallest values and make sure the result is larger than the third value.
Pythagorean theorem
a squared plus b squared equals c squared. the hypotenuse is always c.
Angles
acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles are between 90 and 180 degrees. Straight angles are 180 degrees and reflex angles are greater than 180 degrees.
Triangles classified by angles
acute triangles have 3 acute angles. right triangles have a 90 degree and 2 acute angles. obtuse triangles have an obtuse and 2 acute angles.
Alternate interior angles
alternate interior angles are congruent.
Vertical angles
angles whose sides create two pairs of opposite rays. They are always congruent.
Skew Lines
are lines on different planes that never touch.
Parallel lines
are lines on the same plane that never touch.
Collinear points
are points that lie on the same line
Coplanar points
are points that lie on the same plane
Angle bisector
bisects an angle into 2 congruent angles. they meet in a triangle at a point called the incenter.
Perpendicular bisector
bisects and makes a right angle with a side of a triangle.They meet in a triangle at a point called the circumcenter.
Median
bisects the opposite side into 2 congruent line segments. they meet in a triangle at a point called the centroid. median segments are in a ratio of 2 to 1.
Conditional Statements and related conditionals
conditional, converse, inverse, contrapositive
Corresponding angles
corresponding angles are congruent.
Perimeter
distance around the outside of a polygon.
Point
has no length, width, or thickness. It is indentified by a capital letter.
Line
has no thickness, but it extends forever in both directions.
Slopes of parallel lines
have the same slope and a different y intercept.
Law of Syllogism
if p-->q and q-->r, then p-->r
Altitude
makes a right angle with the opposite side. they meet in a triangle at a point called the orthocenter.
The Law of Detachment
p-->q and p is true, therefore q must be true
Triangles classified by sides
scalene triangles have no equal sides. isosceles triangles have at least 2 equal sides. equilateral triangles have 3 equal sides.
Adjacent angles
share a common vertex, a common side, but not common interior points.
Isosceles triangles
sides opposite congruent angles in triangle are congruent. angles opposite congruent sides are congruent.(Base Angles of an isosceles triangle are congruent.)
Triangle Angle Sum
the 3 angles of a triangle add up to 180 degrees.
Exterior angle of a triangle
the exterior angle of a triangle equals the sum of the 2 opposite interior angles.
Slopes of perpendicular lines
the slopes are opposite reciprocals. to find the opposite reciprocal make the slope a fraction, flip it, and change the sign.
Distance formula
the square root of x two minus x one squared plus y two minus y one squared. (the square root of horizontal change squared plus vertical change squared on the coordinate plane)
Midpoint formula
x one plus x two divided by two is the x coordinate. y one plus y two divided by two is the y coordinate. (The average of the two endpoints)
Slope formula
y two minus y one divided by x two minus x one. rise over run.