Midterm Flashcards
Vertical Angels Congruence Theorem
All vertical angles are congruent
Right angle congruence theorem
All right angles are congruent
Linear Pair postulate
Angles In a linear pair are supplements
Parallel lines
Lines that don’t intersect and slopes are equal
Skew Lines
Do not intersect and aren’t on the same plane
Parallel Postulate
Given a line and a point not on the line, you can draw only one line that is parallel to the original line and goes through the point
Perpendicular postulate
Given a line and a point not on the line, you can only draw one line that is perpendicular to the original line and goes through the point
Transversal
A line that intersects 2 or more other lines at different points
Interior angles
Inside the lines
Exterior angles
Outside the lines
Consecutive interior angles
Inside the lines and on the same side of the transversal
Alternate interior angels
Inside the lines and Opposite sides of the transversal
Alternate exterior angles
Outside the lines, opposite sides of the transversal
Corresponding angles
One inside one outside the lines, not adjacent (different intersections) same Sid of the transversal
Consecutive interior angles postulate
For parallel lines crossed by a transversal, consecutive interior angles are supplementary
Alternate interior angles postulate
For parallel lines crossed by a transversal, alternate interior angles are congruent.
Corresponding angles postulate
Corresponding angles are congruent
Converse
Reversing (switching) the two parts of an if-then statements
Consecutive interior angles converse theorem
For lines cut by the transversal, if their consecutive interior angles are supplements, then the lines are parallel
Alternate interior angles converse theorem
For lines cut by the transversal, if their alternate interior angles are congruent, then the lines are parallel
Alternate exterior angles converse theorem
For lines cut by the transversal, if their alternate exterior angles are congruent, then the lines are parallel
Corresponding angles converse theorem
For lines cut by the transversal, if their corresponding angles are congruent, then the lines are parallel
Transitive property of parallel lines
If a is parallel to b, and b is parallel to c, then a is parallel to c
Slope intercept of a line
Y=mx+b
Y intercept
B (as in y=mx+b)
Slope
Rise over run, change in y over change in x
H0Y VUX
Horizontal line, 0 slope, Y=#
Vertical line, undefined slope, x=#
Steepness
How fast the incline is rising(slope)
Slopes of parallel lines
Identical
Slopes of perpendicular lines
Opposite and reciprocal
Opposite reciprocals
Ex) 3/4 would be -4/3
Perpendicular transversal theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
Scalene
No sides are congruent
Isosceles
2 sides are congruent
Equilateral
All three sides are congruent
Vertex
The angle created by two legs
Legs on an isosceles triangle
The two congruent sides
Isosceles base
The non-congruent side
Isosceles base angles
The 2 angles adjacent to the base
Acute triangle
All angles less than 90 degrees
Equiangular
All angles are congruent
Obtuse
One angle is greater than 90 degrees
Right
One right angle
Triangle sum theorem
The interior angles of a triangle add up to 180 degrees
Corollary
An extension of a theorem/postulate
Triangle sum corollary
The sum of the acute angles in a right triangle is 90 degrees
Remote interior angles
The two interior angles not adjacent to the exterior angle
Exterior angle theorem
The measure of an exterior angle equals the sum of the remote interior angles
Congruent polygons
Have the same shape and size
Corresponding parts of triangles
The same side or angle in 2 different triangles
Congruent triangles
If 2 triangles have 3 pairs of congruent corresponding angles and 3 pairs of congruent corresponding sides, the triangles are congruent
CPCTC
Corresponding parts of congruent triangles are congruent theorem.
Symmetric property of congruent triangles
If triangle abc is congruent to triangle def, then def is congruent to abc
Transitive property of congruent triangles
If abc is congruent to def, and def is congruent to jkl, then jkl is congruent to abc
Reflexive property of congruent triangles
Abc is congruent to abc
Third angle theorem
if 2 angles of a triangle are congruent to 2 angles of another triangle, then the third angles are automatically congruent
What are the six ways to prove triangles congruent
CPCTC, SSS, SAS, AAA, AAS, HL
Included angle
The angle between 2 sides
Hypotenuse
The side across from the right angle
Leg
The sides of the right triangle(not hypotenuse)
Non-included side
A side not between 2 angles
Base
The non-congruent side
Base angles
The 2 angles adjacent to the base
Base angle theorem
If 2 sides of a triangle are congruent, then the angles opposite from them are congruent
Converse of the base angle theorem
If two angles of a triangle are congruent, then the sides opposite from them are congruent
Mid segment of Triangle
Segment that connects midpoints of two sides of a triangle
Mid segment theorem
The segments connecting the midpoints of two sides of a triangle are parallel and half as long as the third side
Equidistant
A point the same distance from 2 points
Perpendicular bisector
A segment that is perpendicular to the segment at its midpoint
Perpendicular bisector theorem
If a point is on the perpendicular bisector of a segment then it is equidistant from the end points of a segment
Converse of perpendicular theorem
If a point is equidistant from the end points of a segment, then it is on the perpendicular bisector of a segment
Angle bisector
A ray that divides an angle into two congruent adjacent angles(cuts it in half)
Distance From a point to a line
The length of the perpendicular segment from a point to a line
Angle bisector theorem
If a point is on the angle bisector of an angle, then it is equidistant from the two sides of an angle
Converse of angle bisector theorem
If a point inside an angle is equidistant from the two sides of the angle, then it is on the angle bisector of the angle.
Altitude
A line segment that connects a vertex of a triangle with the opposite side,(or line containing the opposite side) and is perpendicular to that side
Median
A line segment that connects a vertex of a triangle with the midpoint of the opposite side (3 per triangle)
Triangle inequality theorem
A-b<a+b
Ratios
Comparison of two numbers Using division
Extended ratios
More than 2 numbers In a ratio
Perimeter formula for a rectangle
2(x)+2(y)
Area formula for a rectangle
(X)(y)
Proportion
2 or more ratios in an equation
Congruent polygons
Same size, same shape
Similar(~) polygons
Corresponding angles are congruent and have same proportion, can be different sizes
Statement of proportionality
Pretty much CPCTC
Scale factor
The ratio of the lengths of two Corresponding sides
Similarity of other lengths theorem
When all ratios turn out equal =
AA similarity postulate
If 2 sets of corresponding angles are congruent then the triangles are similar
SSS Similarity theorem
When you prove triangles similar by having all sides congruent
SAS similarity theorem
When you prove triangles similar by having a side, angle, and side congruent
Side splitter theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the other two side proportionally
Converse of the side splitter theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the third side
side splitter theorem extended
If three parallel lines intersect two transversals, then they divide the transversals proportionately
Angle bisector theorem
If a ray bisects an angle of a triangle, then it divided the opposite sides into segments proportional to their adjacent sides
Radicand
The number under the radical
Pythagorean theorem
A^2+b^2=c^2
Pythagorean triples
Sets of positive numbers that satisfy the Pythagorean theorem
Converse of the Pythagorean theorem
If the sum of the squares of the shorter sides of a triangle equals the square of the longest side, then it is a right triangle
Acute triangle theorem
If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is acute
Obtuse triangle theorem
If the square of the longest side of a triangle is more than the sum of the squares of the other two sides, then the triangle is obtuse
Complimentary angles
Adding up to 90 degrees
Supplementary angles
Add up to 180 degrees
