Geometry: Unit 4 Review

Reasoning & Truth Values

100

What is next in the pattern? 5, -2, -9, -16,...

-23

200

Show that the conjecture is false by finding a counterexample. For any integer n, n^3 > 0.

Anything n <= 0

300

Determine if the conditional is true. If false, give a counterexample: If a triangle has two acute angles, it is an acute triangle.

False (third angle does not have to be acute)

400

Determine whether the conjecture is valid by the Law of Detachment. Given: If Lewis earns a scholarship, he can go to college. Lewis earns a scholarship. Conjecture: Lewis can go to college.

True

500

Determine whether the conjecture is valid by the Law of Syllogism: Given: If a whole number ends in 0, then it is divisible by 2. If a whole number is divisible by 2, then it is even. Conjecture: If a whole number ends in 0, then it is an even number.

True

Conditionals and Their Buddies

100

Rewrite the statement in its conditional form: When it rains, there are clouds in the sky.

If it is raining, then there are clouds in the sky.

200

Write the converse of the statement: "If two angles are congruent, then they have the same measure."

If two angles have the same measure, then they are congruent.

300

Write the statement as a biconditional: A square is a rectangle with four congruent sides.

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

400

Write the contrapositive of the statement: "If two angles are supplements of the same angle then the angles have the same measure."

"If two angles do not have the same measure, then they are not supplements of the same angle."

500

Determine whether the biconditional statement is true. If false, give a counterexample. "It is Monday if and only if it is not the weekend."

Nope--it could be Tuesday (non-weekend), which is not Monday.

Algebraic Proof

100

Solve the equation and write a justification for each step. x + 5 = 12

Given

Subtraction Property

200

Solve the equation. Write a justification for each step. 5m - 3 = 22

Given

Addition Property

Division Property

300

Write a justification for each step: 4(x - 7) = 3x + 8

(1) 4(x - 7) = 3x + 8

(2) 4x - 28 = 3x + 8

(3) 4x - 36 = 3x

(4) -36 = -x

(5) 36 = x

(1) Given

(2) Distributive Property

(3) Subtraction Property

(4) Subtraction Property

(5) Division Property (or Multiplication Property)

400

Given: 18x - 2(3x + 1) = 5x - 16

Prove: x = -2

(1) 18x - 2(3x + 1) = 5x - 16

(2) 18x - 6x - 2 = 5x - 16

(3) 12x - 2 = 5x - 16

(4) 7x - 2 = -16

(5) 7x = -14

(6) x = -2

(1) Given

(2) Distributive Property

(3) Simplify

(4) Subtraction Property

(5) Addition Property

(6) Division Property

500

Which properties are used in the following solution: 18x - 2(3x + 1) = 5x - 16

(Work must be shown)

Given, Distributive Property, Simplify, Subtraction Property and Division Property.

Geometric Proof

100

Use the Reflexive Property of Congruence to compete the statement: "Angle A ~= _________"

Angle A

200

What reason should be given for the following progression of statements in a proof? 1) Angle 1 ~= Angle 2, Angle 2 ~= Angle 3 (Given) 2) mAngle 1 = mAngle 2 and mAngle 2 = mAngle 3 (?)

Definition of Congruent Angles

300

Use the Transitive Property of Congruence to complete the statement "If segment AB ~= segment CD and segment CD ~= segment EF, then ___________."

Segment AB ~= segment EF

400

What reason should be given for the following statements? J is in the interior of angle MKL. (Given) Angle MKJ ~= Angle JKL (?)

Angle addition postulate

500

Given: <1 & <2 form a linear pair; 

          m<2 + m<3  = 180

Prove: <1 ~= <3

(1) <1 & <2 form a linear pair

(2) <1 & <2 are supplementary

(3) m<2 + m<3  = 180

(4) <2 & <3 are supplementary

(5) <1 ~= <3

Given

Linear Pair (Supplement) Theorem

Given

Def of Supplementary Angles

Congruent Supplements Theorem

Random Trivia

100

The measures of two angles are equal if and only if the angles are congruent. What definition, property, postulate, or theorem am I?

Definition of Congruence

200

If two angles complementary to the same angle, then they are congruent? What definition, property, postulate or theorem am I?

Congruent Complement Theorem

300

The following are two angles located on the same side of the transversal enclosed by parallel lines. 

96 degrees

6x - 30

Solve for x and state the converse.

x = 19

Consecutive Interior Angles

400

Given: <1 & <4 form a linear pair; <1 & <2 are supplementary.

Prove: <3 ~= <4

(1) <1 & <4 form a linear pair

(2) <1 & <4 are supplementary

(3) <1 & <2 are supplementary 

(4) <4 ~= <2

(5) <2 ~= <3

(6) <3 ~= <4

(1) Given (2) Linear Pair (Supplement) Theorem (3) Given (4) Congruent Supplements Theorem (5) Vertical Angles Theorem (6) Transitive Property

500

Given: Segment AB is congruent to segment CD

Prove: Segment AC is congruent to segment BD

(1) Segment AB ~= Segment ~CD

(2) AB = CD

(3) AC + CD = AD; AB + BD = AD

(4) CD + BD = AD

(5) AC + CD = CD + BD

(6) AC = BD

(7) Segment AC ~= Segment BD

(1) Given (2) Def of Congruence (3) Segment Addition Postulate (4) Substitution (5) Transitive Property (6) Subtraction Property (7) Def of Congruence