Honors Geometry Semester 1 Exam

Collinear Points

Points that lie on the same line

Coplanar Points

Points that lie on the same plane

Opposite Rays

Two rays that share the same endpoint and form a line

Intersection

Set of points that figures have in common

Postulate

A rule that is accepted without proof

Theorem

A rule that can be proved

Between

A point is between two lines only if they are collinear

Segment Addition Postulate

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

Midpoint

The point that divides segments into two congruent segments

Segment Bisector

A point, ray, line, line segment, or plane that intersects the segment midpoint

Midpoint Formula

X1+X2/2, Y1+Y2/2

Distance Formula

(X2-X1)2 + (Y2-Y1)2

Acute Angle

Greater than 0, Smaller than 90

Right Angle

90

Obtuse

Greater than 90, Smaller than 180

Straight

180

Angle Addition Postulate

If two smaller angles that make a larger angle, you can find the degree of the larger angle by adding the smaller angles together

Angle bisector

A ray that divides an angle into two congruent angles

Complementary Angles

Two angles whose sum is 90

Supplementary Angles

Two angles whose sum is 180

Adjacent Angles

Two angles who share a common vertex and side but have no common interior points

Linear Pair

Two adjacent angles whose non common sides are opposite rays

Vertical Angles

Two angles whose sides form two pairs of opposite rays

Polygon

-Closed plane figure

-formed by 3 or more lines

-each side intersects exactly two sides, one at each endpoint, so no sides are collinear

-name them in the order the vertices go

Convex Polygon

A polygon with no line that contains a side of the polygon also containing points on the interior of the polygon

Concave Polygon

Not convex

Equilateral

A polygon with all sides congruent

Equiangular

A polygon with all angles congruent

Regular polygon

A convex polygon that is both equiangular and equilateral

Conjecture

An unproven statement that is based on observations

Inductive Reasoning

Using patterns and observations to write a conjecture (draw a conclusion)

Counterexample

A specific case for which the conjecture is false, proving it false

Conditional Statement

A logical statement that has two parts, a hypothesis and conclusion (if/then)

Biconditional Statements

A statement that contains "if and only if" statement whose converse is true

Deductive Reasoning

Using facts, definitions, accepted properties and the laws of logic to construct a logical argument

Reflexive Property

AB = AB

Symmetric Property

BA = AB

Right Angles Congruence Theorem

All right angles are congruent

Congruence Supplements Theorem

If two angles are supplementary to the same angle, then they are congruent

Congruent Complements Theorem

If two angles are complementary to the same angle, then they are congruent

Linear Pair Postulate

If two angles form a linear Pair, then they are supplementary

Vertical Angles Congruence Theorem

Vertical angles are congruent

Parallel Lines

Coplanar and don't intersect

Skew Lines

Not coplanar and don't intersect

Parallel Planes

Planes do not intersect

Parallel Postulate

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

Perpendicular Postulate

If there is a line not on the line, then there is exactly one line through the point perpendicular to the given line

Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then the pair of corresponding angles are congruent

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pair of alternate interior angles are congruent

Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the pair of alternate exterior angles are congruent

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pair of consecutive interior angles angles are supplementary

Corresponding Angles Converse

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 Exterior Angles 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, them they are parallel to each other

Slope

Ratio of change in x over the change in y

Slope of Parallel Lines Postulate

Two nonvertical lines are Parallel if they have the same slope.

Slope of Perpendicular Lines Postulate

In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slopes is -1

Slope Intercept Form

y=mx+b

Point-Slope Form

y-y^1 = m(x-x^1)

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 4 right angles

If two sides of two adjacent angles are perpendicular

Then the angles are complementary

Perpendicular transversal Theorem

If a transversal is perpendicular to one or two Parallel loses, them it is perpendicular to the other

Lines perpendicular to a transversal Theorem

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

The length of the perpendicular segment from the point to a line

Scalene

No congruent side lengths

Isosceles

At least 2 congruent sides

Equilateral

3 congruent sides

Acute

3 acute angles

Right

1 right angle

Obtuse

1 obtuse angle

Equiangular

3 congruent angles

Triangle sum Theorem

The sum of the measures of the interior Angles of a triangle is 180 degrees

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the same of the measure of the non adjacent interior angles

Corollary of the triangle sum Theorem

The acute angles of a right triangle are complementary

Congruent figures

All parts in one figure are congruent to the corresponding parts of another figure

Third angles Theorem

If two angles of one triangle are congruent to two angles of another triangle, the third angle angles are also congruent

Side-Side-Side Congruence Postulate

If three sides of one triangle are congruent to three sides of a second triangle, then the two angles are congruent

Side-Angle-Side Congruence Postulate

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, they're congruent

Hypotenuse-Leg Congruence Theorem

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a right leg to a second right triangle, they're congruent

Angle-Side-Angle Congruence Theorem

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then they're congruent

Angle-Angle-Side

If two angles and a non included side of triangle are congruent to two angles and the corresponding non included side of a second triangle, them they're congruent

CPCTC

Corresponding Parts of Congruent Triangles are Congruent

Legs (isosceles)

The two congruent sides

Vertex angle

Angle formed by legs

Base

Third side of triangle

Base angles

Two angle adjacent to the base

Base angle Theorem

If two sides of a triangle are congruent then the angles opposite them are congruent

Converse of the base angle Theorem

If two angles of a triangle are congruent, then the sides opposite them are congruent

Corollary to the base angle Theorem

If a triangle is equilateral, than it is equilangular

Corollary to the Converse of the base angles Theorem

If a triangle is equiangular, then it is equilateral