Vocabulary
A ray
It has one definite endpoint and one side that extends indefinitely
May we assume straight lines and angles
yes
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
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
What is the inverse of the following:
"If James is hungry, he will eat."
If James is not hungry, he will not eat.
An angle
Two rays with a common endpoint
May we assume right angles
no
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)
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
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."
Implication
A conditional statement
May we assume congruency
no
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)
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.
What is the logical equivalent to a conditional statement?
Its contrapositive
Negation
May we assume colinearity
yes
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)
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.
What is the probability formula?
Number of winners over number of possibilities
Contrapositive
If ~ q, then ~ p
Which of the following may we assume:
The relative position of points
or Relative sizes of segments and angles
The relative position of points
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)
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
Define and exemplify chain reasoning
A series of steps in a logical sequence. If p=q and q=r then p=r