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Gravity
Key Concepts:
Terms in this set (65)
Collinear
Points that lie on the same line
Linear Pair
A pair of adjacent angles whose noncommon sides are opposite rays.
Supplementary angles
Two angles whose sum is 180 degrees
Vertical Angles
A pair of opposite congruent angles formed by intersecting lines
Angle addition postulate
If P is in the interior of <RST, then m<RSP + m<PST = m<RST
Segment addition postulate
If B is between A and C, then AB + BC = AC
Congruent
Having the same size and shape
Angle bisector
a ray that divides an angle into two congruent angles
Segment bisector
a segment, ray, line, or plane that intersects a segment at its midpoint
Midpoint
A point that divides a segment into two congruent segments
parallel lines
lines in the same plane that never intersect
conditional statements
A statement that can be written in if-then form.
hypothesis
A testable prediction, often implied by a theory
An educated guess
conclusion
A summary based on evidence or facts
triangle sum theorem
The sum of the measures of the interior angles of a triangle is 180 degrees
Transitive property
If a=b and b=c, then a=c
Substitution property
If a=b, then a can be substituted for b in any equation or expression
Line segment
A part of a line with two endpoints
Line
Extends in both directions. Has no end. Named by any 2 points that lie on its. Arrows on both ends
transversal
a line that intersects two or more coplanar lines at different points
corresponding angles
Angles formed by a transversal cutting through 2 or more lines that are in the same relative position.
same side interior angles
two interior angles on the same side of the transversal
same side exterior angles
two exterior angles on the same side of the transversal
alternate interior angles
angles between 2 lines and on opposite sides of a transversal
alternate exterior angles
Angles that lie outside a pair of lines and on opposite sides of a transversal.
Regular triangle
All congruent sides and angles
Quadrilateral
A flat shape with four straight sides. (closed)
regular polygon
A polygon is regular when all angles are equal and all sides are equal (otherwise it is "irregular").
irregular polygon
A polygon that does not have all sides equal and all angles equal.
perpendicular lines
Lines that intersect to form right angles
adjacent angles
Two angles that share a common side and have the same vertex
coplanar
points that lie on the same plane
complementary angles
Two angles whose measures add to 90 degrees.
distance
How far it is from one point to another
ray, opposite rays
a part of a line that starts at one endpoint and extends forever
Pythagorean Theorem
In a right angled triangle: the square of the hypotenuse is equal to. the sum of the squares of the other two sides.
Corresponding Angles Postulate- If two parallel lines are cut by a transversal,...
Then the pairs of corresponding angles are congruent.
Alternate Interior Angles Theorem- If two parallel lines are cut by a transversal,...
Then the pairs of alternate interior angles are congruent.
Alternate Exterior Angles Theorem- If two parallel lines are cut by a transversal,...
Then the pairs of alternate exterior angles are congruent.
Consecutive Interior Angles Theorem- If two parallel lines are cut by a transversal,...
Then the pairs of consecutive interior angles are supplementary.
Corresponding Angles Converse Postulate- If two lines are cut by a transversal so the corresponding angles are congruent, ...
Then the lines are parallel.
Alternate Interior Angles Converse- If two lines are cut by a transversal so the alternate interior angles are congruent, ...
Then the lines are parallel.
Alternate Exterior Angles Converse- If two lines are cut by a transversal so the alternate exterior angles are congruent, ...
Then the lines are parallel.
Consecutive Interior Angles Converse- If two lines are cut by a transversal so the consecutive interior angles are supplementary,
Then the lines are parallel.
Transitive Property of Parallel Lines- If two lines are parallel to the same line,...
Then they are parallel to each other.
Skew Lines
Two lines that do not intersect and are not coplanar.
Slope
Ratio of vertical change (rise) to horizontal change (run) Rise/Run; (y2-y1)/(x2-x1)
Slopes of Parallel Lines
If and only if they have the same slope.
Slopes of Perpendicular Lines
If and only if the product of their slopes is -1 (Opposite Reciprocals) Horizontal lines are perpendicular to Vertical Lines
Slope Intercept Form
y=mx+b
m
Slope
b
Y- intercept
Write Equation of a Line
1. Find the slope. If parallel- same, if Perpendicular- Opposite Reciprocals.
2. Find the y-intercept. On graph- Where line crosses y-axis. Equation- substitute for m, x and y using the point given, solve for b.
3. Plug m (slope) and b (y-intercept) into equation y=mx+b
Standard Form
Ax+By=C (To graph: Find x and y intercepts, plot points on the x and y axis, and connect!)
If two lines intersect to form a linear pair of congruent angles,
then the lines are perpendicular.
If two lines are perpendicular,
then they intersect to form four right angles.
If two sides of two adjacent acute angles are perpendicular,
then the angles are complementary.
If a transversal is perpendicular to one of two parallel lines,
then it is perpendicular to the other.
In a plane, if two lines are perpendicular to the same line,
then they are parallel to each other.
Distance from a point to a line
Length of the perpendicular segment from the point to the line.
Perpendicular Lines
Two lines that intersect to form a right angle
Right Angle
An angle with measure equal to 90 degrees
Vertical Angles
Two angles whose sides form two pairs of opposite rays - (Vertical Angles are congruent)
Supplementary Angles
Two angles whose measure have the sum 180 degrees
Linear Pair
Two adjacent angles whose noncommon sides are opposite rays
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