Geometry Honors Unit 1 Test

Addition property of equality

If you add the same number to both sides of an equation, the sides remain equal. c+b=a+b

Subtraction property of equality

If you subtract the same number from both sides of an equation, the sides remain equal. c-b=a-b

Multiplication property of equality

If you multiply both sides of an equation by the same non-zero number, the sides remain equal. cb=ab

Division property of equality

If you divide both sides of an equation by the same non-zero number, the sides remain equal. c/b=a/b

Inverse property of equality

Combining a number with its inverse returns the identity element of that operation. b+-b=0

Commutative property (add or multiply)

You can change the order of numbers in addition or multiplication without changing the result. a+b=b+a

Associative property (add or multiply)

How you group numbers in addition or multiplication does not change the result. (a+b)+c=a+(b+c)

Distributive property

The sum of the products is equal to the product of the sums.

Reflexive property

Any quantity, value, or geometric figure is equal and congruent to itself. a=a

Symmetric property

If one quantity or expression equals another, you can swap their positions across the equal sign and the statement remains true. x=5, 5=x, a=b, b=a

Transitive property

 If a = b and b = c, then c = a; this can continue infinitely.

Substitution property

If a=b, then a can be substituted for b in any equation without changing its value. 

Identity property of addition/multiplication

Combining any number with a special identity element leaves the original value left unchanged. a+0=a

Multiplicative property of 0

The product of any number and zero is always zero. a x 0= 0

Zero product property

If the product of two or more numbers or expressions is zero, then at least one of those factors must be equal to zero. If ab=0, then a=0, b=0, or both equal zero.

A line contains at least

two points

a plane contains at least

three points not on a line

space contains at least

four points not all in one plane

Through any two points there is

exactly one line

Through any three points there is

at least one plane

through any three noncollinear points there is

exactly one plane

 If two points are in a plane, then the line that contains the points is

also in that plane

If two planes intersect, then their intersection is

a line

If two lines intersect, then they intersect in

exactly one point

Through a line and a point not on the line, there is

exactly one plane

If two lines intersect, then

exactly one plane contains the lines

Ruler Postulate

1.  The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0-1.

2. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates.

Segment Addition Postulate

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

Protractor Postulate

1. Three collinear points, A, O, B form opposite rays OA and OB. Ray OA is paired with 0, and ray OB is paired with 180, and any ray from O can measure an angle from 0 to 180.

2. If ray OP is paired with some degree measure and ray OQ is paired with another measure, then the of m∠POQ=l x-y l

Angle Addition Postulate

If point B lies inside angle AOC, then the measure of angle AOB+angle BOC= angle AOC.

Linear Pair Postulate

If ∠AOC is a straight angle and B is not on line AC, then m∠AOB+m∠BOC=180 degrees

Adjacent angles

two angles in a plane that share a common vertex and a common side but no common interior points

Midpoint Theorem

If a point M is the midpoint of a line segment AB, then AM=1/2AB and BM=1/2AB

Angle Bisector Theorem

If ray BX is the bisector of ∠ABC, then m∠ABC=1/2m∠ABC and m∠XBC=1/2m∠ABC

Complementary Angles

two angles whose measures have a sum of 90 degrees. 

Supplementary Angles

two angles whose measures have a sum of 180 degrees.

Vertical Angles

two angles such that the sides of one angle are opposite rays to the sides of the other angle. When two lines intersect, they form vertical angles.

Biconditional Statement About Perpendicular Lines/Congruent Adjacent Angles

Two lines are perpendicular if and only if they form congruent adjacent angles.

Theorem About Adjacent Acute Angles and Complementary Angles

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

Complements Theorem

If 2 angles are complementary to congruent angles, then they are congruent.

Supplements Theorem

If 2 angles are supplementary to congruent angles, then they are congruent.

 If two parallel planes are intersected by a third plane, then

the lines of intersection are parallel.

Transversal

a line that intersects two or more coplanar lines in different points.

Alternate interior angles

two non-adjacent interior angles on opposite sides of the transversal.

• (3, 10)

• (4, 9)

• (7, 14)

• (8, 13)

Alternate exterior angles

two non-adjacent exterior angles on opposite sides of the transversal.

• (1, 12)

• (2, 11)

• (5, 16)

• (6, 15)

Same-side interior angles

two interior angles on the same side of the transversal.

• (3, 9)

• (4, 10)

• (7, 13)

• (8, 14)

Same-side exterior angles

two exterior angles on the same side of the transversal.

• (1, 11)

• (2, 12)

• (5, 15)

• (6, 16)

Corresponding angles

two angles in corresponding positions relative to the two lines.

• (1, 9)

• (2, 10)

• (3, 11)

• (4, 12)

• (5, 13)

• (6, 14)

• (7, 15)

• (8, 16)

Parallel Line Postulate

If two lines are parallel and intersected by a transversal, then corresponding angles are congruent.

If two lines are parallel and intersected by a transversal, then

alternate interior/exterior angles are congruent.

If two lines are parallel and intersected by a transversal, then

same-side interior/exterior angles are supplementary.

Two parallel lines are perpendicular to the same transversal.

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Two lines parallel to a third line are parallel to each other. (not transitive)

If a is parallel to b and b is parallel to c, then a is parallel to c.

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