Geometry Logic & Proofs

Properties

100

If    4x=24

then    x=6

Division Property of Equality

200

If angle A is congruent to angle C

and angle C is congruent to angle F,

then angle A is congruent to angle F.

Transitive Property of Equality

300

If a=-4

then 6a+2 = 6(-4)+2

Substitution Property

400

If  PR = QS  and  PQ + QR = PR

then QS = PQ + QR

Transitive Property of Equality

(or Substitution Property)

500

3(x-4) = 3x - 12

Distributive Property

Conditional Statements

100

Provide a counterexample to this FALSE conditional statement:

"If a number is a perfect square, then it is divisible by 2"

Possible answers:

9, 25, 49, 81, 121

200

What is the truth value of the INVERSE of this statement?

"If 2x=12, then x is greater than 5."

False

300

What is the CONVERSE of this conditional statement?

"If a month begins with the letter M, then it has 31 days."

If a month has 31 days, then it begins with the letter M.

400

What is the biconditional statement of this conditional statement?

"If a rectangle has four congruent sides, then it is a square."

"A rectangle is a square if and only if it has four congruent sides."

500

What is the contrapositive statement of'

"If a figure has four sides, then it is a square."

"If a figure is not a square, then it does not have four sides."

Postulates & Theorems

100

If point B is on line segment AC,

then AB + BC = AC

Segment Addition Postulate

200

True or False:

The Definition of Congruency says that congruent angles have equal measures.

True

300

If two angles are congruent AND supplementary, then each angle is ___________.

a right angle (90 degrees)

400

What theorem is used here?

If two angles form a linear pair, then they are supplementary.

Linear Pair Theorem

(aka Supplement Theorem)

500

What Theorem is used here?

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

Congruent Supplements Theorem

Proofs

100

What reason should be on the first line of a proof?

GIVEN

200

Give an example of the Transitive Property of Congruence

Answers will vary - Ms. Frey will judge

300

What reason would you give for the following statement:

m<ABD + m<DBC = m<ABC"

Angle Addition Postulate

400

Given: 10 = 2x - 6

What FOUR reasons will be needed in a two-column proof to prove that x=8?

Given

Addition Property of Equality

Division Property of Equality

Symmetric Property

500

When proving B is the midpoint of segment AC, what statement would be on the line above it in a proof?

AB=BC