FIRST SIX WEEKS REVIEW

SYMBOLS & TERMS

A B 6 SEGMENT Endpoints A and B

A B M M is the Midpoint of 3 3

A segment has endpoints on a number line of -3 and 5, Find its length.

A segment has endpoints on a number line of -3 and 5, find its midpoint.

The Midpoint of a segment

Find the midpoint of the segment joining (3,4) and (-5,-6).

Pythagorean Theorem– Used to find a missing side of a right triangle.

If a=5, and b=12, then c=_?_ 13

The distance formula—for finding the length of a segment.

Find the distance between (-2,-6) and (4, 2):

Find the distance between (2,-6) and (-4, 2):

ACUTE Angle Less than 90

OBTUSE Angle Greater than 90 but less than 180

RIGHT Angle Equals 90

STRAIGHT Angle Equals 180

SPECIAL PAIRS OF ANGLES

Nonadjacent Angles

B C A D For adjacent angles

B C A D

B C A D

Supplementary Angles A B

Vertical Angles

Also Vertical Angles

Linear Pair

Complementary Angles A B

Congruent Angles A B

Angle Bisector B C

Conditional Statement: Any statement that is or can be written in if- then form. That is, If p then q.

Symbolically we use the following for the conditional statement: “If p then q”:

EXAMPLE: If you feed the dog, then you may go to the movies.

EXAMPLE: If you feed the dog, then you may go to the movies. Hypothesis

EXAMPLE: If you feed the dog, then you may go to the movies. Hypothesis Conclusion

“ALL” Statements: When changing an “all” statement to if-then form, the hypothesis must be made singular.

EXAMPLE: All rectangles have four sides. BECOMES: If _______ a rectangle then _____ four sides. a figure is it has

The Converse: The conditional statement formed by interchanging the hypothesis and conclusion.

Symbolically, for the conditional statement: The converse is:

EXAMPLE: Form the converse of: IfthenX=2X > 0.

EXAMPLE: Form the converse of: IfthenX=2X > 0. IfthenX > 0X=2.

The Inverse: The conditional statement formed by negating both the hypothesis and conclusion.

Symbolically, for the conditional statement: The inverse is:

EXAMPLE: Form the Inverse of: IfthenX=2X > 0. IfthenX=2X > 0.

EXAMPLE: Form the Inverse of: IfthenX=2X > 0. IfthenX=2X > 0.

The Contrapositive: The conditional statement formed by interchanging and negating the hypothesis and conclusion.

Symbolically, for the conditional statement: The contrapositive is:

EXAMPLE: Form the contrapositive of: IfthenX=2X > 0. IfthenX=2X > 0.

LOGIC: SYLLOGISMS

Law of Syllogism

If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect each other. __________________________

If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect each other. __________________________

If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect each other. __________________________

If a figure is a rectangle, then it is a parallelogram. If a figure is a parallelogram, then its diagonals bisect. __________________________ If a figure is a rectangle, then its diagonals bisect.

Law of Detachment

If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________

If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________

If a figure is a rectangle, then it is a parallelogram. ABCD is a rectangle. __________________________ ABCD is a parallelogram.

Law of Contrapositive

If a figure is a rectangle, then it is a parallelogram. ABCD is not a parallelogram. __________________________

If a figure is a rectangle, then it is a parallelogram. ABCD is not a parallelogram. __________________________

If a figure is a rectangle, then it is a parallelogram. ABCD is not a parallelogram. __________________________ ABCD is not a rectangle.

In the following examples, use a law to draw the correct conclusion from the set of premises.

1. If frogs fly then toads talk. Frogs fly

1. If frogs fly then toads talk. Frogs fly Toads talk.

2. If hens heckle then crows don’t care. Crows care

2. If hens heckle then crows don’t care. Crows care Hens don’t heckle.

3. If ants don’t ask then flies don’t fret. Ants don’t ask

3. If ants don’t ask then flies don’t fret. Ants don’t ask Flies don’t fret.

PROPERTIES

IF then

Symmetric Property of Congruence

Reflexive Property of Congruence

IF and then

Transitive Property of Congruence

If and then

Substitution Property of Equality

IF AB = CD Then AB + BC = BC + CD

Addition Property of Equality

If AB + BC= CE andCE = CD + DE then AB + BC = CD + DE

Transitive Property of Equality

If AC = BD then BD = AC.

Symmetric Property of Equality

If AB + AB = AC then 2AB = AC.

Distributive Property

Reflexive Property of Equality

If 2(AM)= 14 then AM=7

Division Property of Equality

If AB + BC = BC + CD then AB = CD.

Subtraction Property of Equality

If AB = 4 then 2(AB) = 8

Multiplication Property of Equality

Let’s see if you remember a few oldies but goodies...

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

The Segment Addition Postulate

If Y is a point in the interior of then

Angle Addition Postulate

IF M is the Midpoint of then

The Definition of Midpoint

IF bisects then

The Definition of an Angle Bisector

If AB = CD then

The Definition of Congruence

If then is a right angle.

The Definition of Right Angle

1 If is a right angle, then the lines are perpendicular.

The Definition of Perpendicular lines.

If Then

The Definition of Congruence

And now a few new ones...

If and are right angles, then

Theorem: All Right angles are congruent.

1 2 If and are congruent, then lines m and n are perpendicular. n m

Theorem: If 2 lines intersect to form congruent adjacent angles, then the lines are perpendicular.