108 terms

# Geometry Final

If needed, use paper to draw out problems and show work.
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A line, a point, or a plane would all be considered an _____?
Undefined Term
A specific case provided to show that a conjecture is false.
Counter Example
Points that lie on the same line are _____?
Collinear
A triangle with two congruent sides.
Isosceles
Points or lines that lie in the same plane.
Coplanar
In <PQR, <Q would be the _____?
Vertex
The inverse of an if-then statement keeps the order the same, but takes the _____ of both parts.
Negation
The ratio of rise to run.
Slope
Two angle sor two segments that have the same measure are considered to be _____?
Congruent
Has one endpoint, but extends forever in the other direction.
Ray
<1 and <2 would be considered _____ exterior angles.
Alternate
A triangle with no congruent sides.
Scalene
For the statement, If you have feathers then you are a bird, the statement If you are not a bird then you do not have feathers would be the _____?
Contrapositive
An angle that measures exactly 180 degrees is a _____ angle.
Straight
This is a segment, ray or line that cuts an angle or segment into two congruent parts.
Bisector
A word that would describe the polygon shown.
Concave
y-y1=m(x-x1) is what form of equation for a line?
Pointslope
Parallel lines have the same _____.
Slope
CPCTC: Corresponding __________ of Congruent Triangles are Congruent.
Parts
The longest side in a right triangle, found opposite the right angle.
Hypotenuse
The angles whose sum is 180 degrees.
Supplementary
These angles are congruent when lines cut by a transversal are parallel.
Corresponding
The formula (x1-x2/2 , y1-y2/2) calculates what?
Mid-Point
The relationship between two lines that intersect to form right angles.
Perpendicular
An angle that measures more than 90 degrees but less than 180 degrees.
Obtuse
In an isosceles triangle, the non-congruent side is the base. Each of the other sides are called _____.
Legs
This type of reasoning uses patterns and observations to form a conjecture.
Inductive
In triangle ABC, m<C = 124 degrees. This work would best describe the triangle.
Obtuse
Lines that are not in the same plane and do not intersect are called _____?
Skew
Opposite of concave.
Convex
In an if-then statement, the "if" represents the hypothesis and the "then" represents the _____.
Conclusion
The point where two lines cross is their point of _____.
Inverse
A polygon that is both equilateral and equiangular.
Regular
A line that intersects two or more lines.
Transversal
Two angles that are supplementary and adjacent are called a _____ pair.
Linear
According to the notations, <---->AB represent a _____.
Line
This is a piece of a line. It can be measured and has two endpoints.
Line segment
If the co-exterior angles are supplementary, then the lines are _____.
Parallel
The _____ Angle Theorem says that the measure of the _____ angle is the sum of the two remote interior angles of a triangle.
Exterior
The new figure created after performing a transformation.
Image
In line KLM, KL=12 and LM=9, so KM=_____.
21
In line STU, SU=22 and TU=4, so ST=_____.
18
In line ABC, AB=x+2 and BC=7x-3, so AC=_____.
8x-1
In line PQR, PR=13y+25 and PQ=8y+5, so QR=_____.
5y+20
The endpoints of line segment are C(6,1) and D(-4,-1). Find the midpoint of CD.
M=(1,0)
On line segment AB, the midpoint is M(-4,-4) and one endpoint is B(-1,-1). Find the other endpoint.
A+(-7,-7)
The endpoints of line segment JK are J(-3,2) and K(9,2). Find the midpoint of JK.
M=(3,2)
On line segment AB, the midpoint is M(2,5) and one endpoint is A(2,3). Find the other endpoint.
B=(2,7)
In line segment SMT, SM=2x+3 and MT=4x-7, so ST=_____.
26
In line segment SMT, SM=3x-6 and MT=x+8, so ST=_____.
30
Find the distance between G(2,5) and H(4,-1).
D=6.3
Find the distance between G(-1,-5) and H(3,-8).
D=5
Two angles form a linear pair. The measure of one angle is twice the measure if the other angle. How much is the larger angle?
120 degrees
The measure of one angle is nine times the measure of its compliment, what is its measure?
81 degrees.
Tell whether the statement is always, sometimes, or never true. Complementary angles are adjacent.
Sometimes
Tell whether the statement is always, sometimes, or never true. Angles in a linear pair are supplements of each other.
Always
Tell whether the statement is always, sometimes, or never true. Vertical angles are adjacent.
Never
Tell whether the statement is always, sometimes, or never true. Vertical angles are supplements of each other.
Sometimes
What is the next letter in the sequence? A, B, D, G, K, ...
P
What is the next number in the sequence? -3, -1, 3, 9, ...
17
What conjecture can be made if John is older than Mark, Sue is older than John, and Betty is younger than Sue?
Sue is the oldest
What is the inverse of the statement... If it rains, then the grass grows.
If it does not rain, then the grass does not grow.
For the statement, Dogs are animals, write the if-then statement.
If it is a dog, then it an animal.
For the statement, Dogs are animals, write the converse statement.
If it is an animal, then it is a dog.
For the statement, Dogs are animals, write the inverse statement.
If it not a dog, then it is not an animal.
For the statement, Dogs are animals, write the contrapositive statement.
If it is not an animal, then it is not a dog.
Using the Transitive Property of Congruency, if <A is congruent to <B, and <B is congruent to <C, then _____.
<A is congruent to <C
What property pf equality is illustrated by the statement? If AB = CD, then CD = AB.
Symmetric
The statement XY is congruent to XY illustrates which property?
Reflexive Property of Congruency
Using the Distributive Property, what is the completion of the statement? If x(x+8)=16, then _____.
x^2+8x=16
Describe the slope of the line passing through the points A(-2,3) and B(4,2).
Negative
Find the slope of the ladder placed 4 feet from the wall and touching the wall at height of 12 feet.
m=3
What is the equation of the line through the point (2,1) and perpendicular to the line through (-4,1) and (3,-2)?
y=7/3x-11/3
Write the equation of the line with a slope = -2 and y-intercept = 3. What is the equation of the line that passes thought the point (-3,5) with a slope of 4.
y=4x+17
If two angles lie between two lines and on opposite sides of a transversal, then the angles are _____.
Alternate Interior Angles
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are _____.
Parallel
Does this figure have any lines of symmetry? If so how many? Does the figure have rotational symmetry? If so, what is the angle of rotation?
One line of symmetry. No rotational symmetry.
Does this figure have any lines of symmetry? If so how many? Does the figure have rotational symmetry? If so, what is the angle of rotation?
Five lines of symmetry. It has rotational symmetry at 72 degrees and 144 degrees.
Does this figure have any lines of symmetry? If so how many? Does the figure have rotational symmetry? If so, what is the angle of rotation?
No lines of symmetry or rotational symmetry.
Classify this triangle based off sides.
Scalene Triangle
Classify this triangle based off sides.
Isosceles Triangle
Classify this triangle based off of sides.
Equilateral Triangle
Classify this triangle based off of angles.
Right Triangle
Classify this triangle based off of angles.
Acute Triangle
Classify this triangle based off of angles.
Obtuse Triangle
The sum of the measures of the interior angles of a triangle is _____.
180 degrees
The sum of the exterior angles of a triangle is equal to the sum of the measures of the two _____ interior angles.
Fill in the blanks.

Given: <PQS is is congruent to <TQR
Prove: <PQT is congruent to <SQR

1) <PQS is congruent to <QRT 1) Given
2) m<PQS=m<TQR 2) _____________
3) m<SQT=m<SQT 3) Reflexive
4) m<PQS+m<SQT=m<TQR+m<SQT
4) _______
5)m<TQR+m<SQT=MSQR m<TQR+m<SQT=m<SQR
5)______
6) m<PQT = m<SQR 6) Transitive
7) <PQT is congruent to <SQR 7) Def. of congruent
2) Definition of Congruent
Fill in the blanks.

Given: RT=SU R------S---T------U
Prove: RS=TU

1) RT=SU 1) Given
2) ST=ST 2) ____________
3) RT-ST=SU-ST 3) Subtraction Property
4) RT-ST=RS 4) ____________
5) SU-ST=TU 5) Segment Addition Postulate
6) RS=TU 6) Transitive Property
2) Reflexive Property
Fill in the blank.

Given: P is parallel to Q
Prove: <1 and <2 are supplementary

1) P is parallel to Q 1) Given
2) <1 is congruent to <3 2) __________
3) m<1 = m<3 3) Def. of Congruent
4) <3 and <2 are supplements 4)__________
5) m<3+m<2=180 degrees 5) Def. of Supplementary
6) m<1+m<2=180 degrees 6) __________
7) <1 and <2 are supplements 7) __________
2) Alternate Interior Angles
4) Linear Pair Postulate
6) Substitution
7) Definition of Supplementary
Fill in the blanks.

Given: G is parallel to H, <1 is congruent to <2
Prove: P is parallel to R

1) G is parallel to H 1) __________
2) <1 is congruent to <2 2) __________
3) <1 is congruent to <3 3) __________
4) <2 is congruent to <3 4) __________
5) P is parallel to R 5) __________
1) Given
2) Given
3) Corresponding Angles Theorem
4) Substitution Property (of Equality)
5) Corresponding Angles Theorem
Write the following definition as a biconditional statement, perpendicular line are lines that intersect to form a right angle.
Lines are perpendicular if and only if they intersect to form a right angle.
Write the next two numbers in the pattern. 9,4,-1,-6,___,___
-11,-16
What is inductive reasoning?
Reaching a conclusion based on a pattern present in numerous observations.
What is deductive reasoning?
Reaching a conclusion based off facts.
State the property, postulate, or theorem that justifies the statement.

If AB=CD and CD=EF, then AB=EF
Transitive Property of Equality
State the property, postulate, or theorem that justifies the statement.

If m<4=m<6, then m<6=m<4
Symmetric Property of Equality
State the property, postulate, or theorem that justifies the statement.

If X lies between A and M, then AX+XM=AM
State the property, postulate, or theorem that justifies the statement.

If m<A=m<B, then m<A+m<C=m<B+m<C
Two angles form a linear pair. If one is twice the measure of the other angle, what is the measure of each angle?

Write the equation AND solve.
x+2x=180

Smaller Angle: 60 degrees
Larger Angle: 120 degrees
Two angles are complementary. The measure of one angle is 4 times the measure of the other angle, what is the measure of each angle.

Write the equation AND solve.
x+4x=90

Smaller Angle: 18 degrees
Larger Angle: 72 degrees
Find the length of the segment, round to the nearest tenth.
A(10,5) and B(2,-3)
AB=11.3
Give the relationship between the pair of angles.
<2 and <6
Corresponding Angles
Give the relationship between the pair of angles.
<1 and <8
Alternate Exterior Angles
Give the relationship between the pair of angles.
<8 and <5
Vertical Angles
Give the relationship between the pair of angles.
<3 and <6
Alternate Interior Angles
Give the relationship between the pair of angles.
<1 and <3
Linear Pair
What is the measure of each angle?
60 degrees