Geometry Ch. 1 Review

Vocabulary

100

A ray

It has one definite endpoint and one side that extends indefinitely 

200

An angle

Two rays with a common endpoint

300

Implication

A conditional statement

400

Negation

~p

500

Contrapositive

If ~ q, then ~ p

Assumptions

100

May we assume straight lines and angles

yes

200

May we assume right angles

no

300

May we assume congruency

no

400

May we assume colinearity 

yes

500

Which of the following may we assume:

The relative position of points

or Relative sizes of segments and angles

The relative position of points

Proofs

100

Given: angle A is a right angle

          angle C is a right angle

Conclusion: angle A is congruent to angle C

(Answer with a 3 s/r proof)

1. Given

2. Given

3. If two angles are right angles then they are congruent

200

Given: Segment DH is congruent to segment HF

Prove: H is the midpoint of DF

DH is congruent to HF (given)

H is the midpoint of DF (If a point divides a segment into two congruent segments it is the midpoint)

300

Given: Angle XYZ is divided into 3 angles (1,2, and 3)

angle 1 is 20

angle 2 is 40

angle 3 is 30

Prove angle XYZ is a right angle

List given, 

Angle XYZ is 90 (addition)

Angle XYZ is a right angle (if an angle is 90 it is a right angle)

400

Given: Angle DEG is congruent to Angle FEG

Prove: Ray EG bisects angle DEF

1) Angle DEG and FEG are gongruent

2) Ray EG bisects angle DEF (if a ray divides an angle into two congruent angles, the ray bisects the angle)

500

Given: angle RSV is divided into two angles, (1 and 2)

          angle 1 is 50 degrees, angle 2 is 40 degrees.

          Angle X is a right angle

Conclusion: Angle RSV and X are congruent 

(Answer with a 6 s/r proof)

Statement:

Angle 1 is 50 (given)

Angle 2 is 40 (given)

Angle RSV is 90 (addition)

Angle RSV is a right angle (if an angle is 90 it is right)

Angle X is a right angle (Given)

Angle RSV is congruent to X (if two angles are right angles, they are congruent)

Algebra

100

Angle ABC is a straight angle divided into two angles (1 and 2) 

Angle 1= x+ 20

Angle 2= 2x

Find the measure of angle 2 (to the nearest whole degree)

107

200

Angle ABC is a right angle divided into 3 angles (1, 2, and 3)

Angle 1 = 2x + 10

Angle 2 = x + 20

Angle 3 = 3x

Find Measure of angle 3

30

300

Describe the 3 main steps to solving for the measure of an angle which is part of a straight angle written as an algebraic expression

Combine all of the angle measurements written as algebraic expressions and set the equation equal to 180 degrees. 

Solve for the variable. 

Substitute into the desired measurement formula.

400

Describe the steps to solving the measure of an angle that is part of right angle and has been written as an algebraic expression

Combine the algebraic expressions on one side 

Set the equation equal to 90 degrees

Solve for the variable

Substitute into the appropriate measure.

500

The measure of angle 1 angle 2 and angle 3 is collectively a straight angle. The angles are in the ratio, 1:3:2. Find the measure of each angle 

30, 90, 60

6x = 180

x= 30

1x= 30

3x= 90

2x= 60

Logic

100

What is the inverse of the following:

"If James is hungry, he will eat."

If James is not hungry, he will not eat.

200

What is the contrapositive of the following:

"I Sharon is a girl, she likes pink."

"If Sharon does not like pink, she is not a girl."

300

What is the logical equivalent to a conditional statement? 

Its contrapositive

400

What is the probability formula?

Number of winners over number of possibilities 

500

Define and exemplify chain reasoning

A series of steps in a logical sequence. If p=q and q=r then p=r