Honors Geometry (KAP) Fall Semester Vocabulary

Reflection

(Flip) Transformation that uses a line of [term] like a mirror to reflect a figure

X-axis

(x,y) -> (x,-y)

Y-axis

(x,y) -> (-x,y)

y=x

(x,y) -> (y,x)

y=-x

(x,y) -> (-y,-x)

General Rule of Reflection

Pre-Image -> Image; Perpendicular to L.O.R and equal distance both sides

Rotation

(Spin) Transformation where a figure is turned around a fixed point

Center of Rotation

Fixed point

(x,y) -> (-y,x)

90 CCW, 270 CW

(x,y) -> (-x,-y)

180 CCW and CW

(x,y) -> (y, -x)

270 CCW, 90 CW

Reflections (non-origin)

When C.O.R is NOT the origin. Start at C.O.R and count "path" using horizontal and vertical. Spin path around C.O.R to create new path to image.

Composition of Transformations

More than one transformation in a row

Glide Reflection

Translation-reflection (L.O.R must be parallel to translation)

Dilation

Grow/shrink a figure to create a similar figure

Scale factor

Multiplier says how much bigger/smaller to make figure

SF > 1

Bigger (enlargement)

SF < 1

Smaller (reduction)

Point

A dot with no dimensions, width, length, or height. One capital letter

Line

Straight with arrows. 1-dimension length, no width and height. 2 capital letters

Plane

Flat infinte surface. 2 dimension length, width, and no height. 3 capital letters or 1 bold capital letter

Colinear

Points on the same line

Coplanar

Figures on the same plane

Intersection

Set of all points 2 or more figures share

Segments

Part of line. 2 endpoints

Congruent

Same shape, same size

Congruent segments

Segments /w equal length

Segment Addition Property

If A, B, C, are colinear and B is between A and C, then AB + BC = AC

Pythagorean theorem

a²+b²=c²

Distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Midpoint

Point that splits a segment into 2 congruent pieces

Segment bisector

A figure that cuts a segment into 2 congruent pieces

Ray

Half a line with one endpoint. 2 capital letters

Opposite Rays

2 rays endpoint /w same endpoint that makes a straight line.

Angle

2 rays /w a common endpoint. 3 letters or 1 letter

Measure of an angle

(Degrees) How big an angle is. Put an "m" in front of your name

Right angle

m = 90

Acute angle

m < 90

Obtuse angle

m > 90

Congruent angles

2 or more angles with the same measure

Angle bisector

A ray that cuts an angle into 2 congruent pieces

Adjacent Angles

Angles that share a side and a vertex with no overlap

Complementary Angles

Add to 90 degrees

Supplementary Angles

Add to 180 degrees

Linear Pair

2 adjacent angles that make a straight line. ALWAYS supplementary

Vertical Angle Pairs

2 angles whose sides form 2 pairs of opposite rays. ALWAYS congruent

Perpendicular

2 lines that intersect and form right angles

Conditional Statement

has two parts, a hypothesis (after if) and a conclusion (after then).

Converse

Formed by switching the hypothesis and conclusion

Contrapositive

Formed by switching and negating the hypothesis and conclusion

Negation

The opposite of the original statement

Inverse

Formed by negating both the hypothesis and conclusion

Equivalent Statements

Two statements that are both true or both false

Biconditional statement:

If a conditional and its converse are both true, then the statement can be written as a biconditional (Hypothesis if and only if Conclusion)

Law of detatchment

(2 statements, 1 if then, 1 not). If 2nd statement confirms hypothesis of if then, then "follow the logic" to the conclusion

Law of syllogism

(2 if then statements) If the hypothesis of one statement matches the core of the other, then rewrite as one if then without the matching pieces

Postulate 1

Through any two points there is exactly one line

Postulate 2

Through any three noncollinear points, there is exactly one plane.

Postulate 3

A line contains at least two points.

Postulate 4

A plane contains at least three noncollinear points

Postulate 5

If two points lie in a plane, then the entire line containing those points lies in the plane

Postulate 6

If two distinct lines intersect, then their intersection is exactly one point

Postulate 7

If two distinct planes intersect, then their intersection is a line

Linear Pairs Postulate

Linear pairs are supplementary

Vertical Angles Congruence Theorem

Vertical angles are congruent

Segment Addition Postulate

B is between A and C -> AB + BC = AC

Angle Addition Postulate

D in interior of m< ABD + m<DBC = m< ABC

Parallel Lines

2 coplanar lines that do not intersect

Skew Lines

Non-coplanar lines that do not intersect

Parallel Planes

2 planes that do not intersect

Parallel Postulate

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the original line.

Transitive Property of Parallel Lines

If 2 lines are parallel to a 3rd line, then they are parallel to each other

Perpendicular lines

2 lines that intersect to form right angles

Perpendicular Planes

2 planes that intersect and form right angles

Transversal

a line that intersects two other lines

Perpendicular Postulate

If there is a line and a point not on the line, then there is exactly 1 line through a point perpendicular to the original line

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other

Lines Perpendicular to a Transversal Theorem

If 2 lines are perpendicular to the same transversal, then they are parallel to each other

Corresponding Angles

Angles in the same relative location

Alternate Interior Angles

Opposite sides of transversal inside other two lines

Alternate Exterior Angles

Opposite sides of transversal, outside other 2 lines

Consecutive Interior Angles

Same side of transversal, inside other 2 lines

Corresponding Angles Theorem (CAT)

The corresponding angles are congruent

Alternate Interior Angles Theorem (AIAT)

The alternate interior angles are congruent

Alternate Exterior Angles Theorem (AEAT)

The alternate exterior angles are congruent

Consecutive Interior Angles Theorem (CIAT)

The consecutive interior angles theorem

Slope intercept form

y = mx + b

Standard form

Ax + By = C

Point slope form

y - y1 = m(x - x1)

Distance from point to line

Shortest distance measured with perpendicular segment

Triangle Sum Theorem

Triangle angles add to 180 degrees

Exterior Angle

Makes a Linear Pair with an interior angle

Remote Interior Angles

2 angles that are NOT a linear pair with exterior

Exterior Angle Theorem

Measure of exterior angle is equal to the sum of the remote interior angles

Isosceles Triangle Theorem

Isosceles if and only if base angles are congruent

Equilateral Triangle Theorem

Equilateral if and only if equiangular

Congruent Polygons

All pairs sides congruent, all pairs angles congruent (same size, same shape)

Corresponding parts

The pairs of congruent things

Third Angles Theorem

In 2 triangles, if there are 2 pairs of congruent angles, then the 3rd pair is also congruent

SSS (Side-Side-Side)

If 3 sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent