Download Geometry Unit 2: Reasoning and Proof Homework Section

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Unit 2: Reasoning and Proof
Geometry
Homework
Section 2.1: Conditional and Biconditional Statements
Write the converse of each conditional.
1.  If you eat spinach, then you are strong.
2.  If a rectangle has four sides the same length, then it is a square.
3.  If you do not study, then you do not earn good grades.
Write the converse of each statement. If the converse is true, write true; if it is not true, provide a
counterexample.
4.  If x - 4 = 22, then x = 26.
5.  If x > 0, then ⎜x⎟ > 0.
6.  If m is positive, then m2 is positive.
7.  If y = 3, then 2y - 1 = 5.
8.  If point A is in the first quadrant of a coordinate grid, then x > 0.
9.  If two lines have equal slopes, then the lines are parallel.
10.  If you are a twin, then you have a sibling.
Each conditional statement is true. Consider each converse. If the converse is true, combine the statements
and write them as a biconditional.
11.  If two angles have the same measure, then they are congruent.
12.  If 2x - 5 = 11, then x = 8.
13.  If n = 17, then ⎜n⎟ = 17.
14.  If a figure has eight sides, then it is an octagon.
Write the two conditional statements that make up each biconditional.
15.  A whole number is a multiple of 5 if and only if its last digit is either a 0 or a 5.
16.  Two lines are perpendicular if and only if they intersect to form four right angles.
17.  You live in Texas if and only if you live in the largest state in the contiguous United States.
REVIEW: Draw a diagram to represent each word.
1. 4 collinear points
2. Opposite rays EA and EB
3. Two adjacent and congruent angles
Section 2.2: Deductive and Inductive Reasoning
Use the Law of Detachment to draw a conclusion.
1.  If the measures of two angles have a sum of 90°, then the angles are complementary. ∠A + ∠B = 90
2.  If the football team wins on Friday night, then practice is canceled for Monday. The football team won
by 7 points on Friday night.
3.  If a triangle has one 90° angle, then the triangle is a right triangle. In ∆DEF,∠E = 90.
Use the Law of Syllogism to draw a conclusion.
4.  If you liked the movie, then you saw a good movie. If you saw a good movie, then you enjoyed yourself.
5.  If two lines are not parallel, then they intersect. If two lines intersect, then they intersect at a point.
6.  If you vacation at the beach, then you must like the ocean. If you like the ocean, then you will like Florida.
If possible, use the Law of Detachment to draw a conclusion. If not possible, write not possible.
7.  If Robbie wants to save money to buy a car, he must get a part-time job. Robbie started a new job
yesterday at a grocery store.
8.  If a person lives in Omaha, then he or she lives in Nebraska. Tamika lives in Omaha.
9.  If two figures are congruent, their areas are equal. The area of ABCD equals the area of PQRS.
Use the Law of Detachment and the Law of Syllogism to draw conclusions from the following statements.
10.  If it is raining, the temperature is greater than 32°F. If the temperature is greater than 32°F, then it is not
freezing outside. It is raining.
11.  If you live in Providence, then you live in Rhode Island. If you live in Rhode Island, then you live in the
smallest state in the United States. Shannon lives in Providence.
12.  If it does not rain, the track team will have practice. If the track team has practice, the team members
will warm up by jogging two miles. It does not rain on Thursday.
REVIEW:
A
1. 
B
Solve for x.
C
AB = 3x + 1 BC = 2x – 3 AC = 23 2. Find AB.
3. Find BC.
Section 2.3: Properties of Equality and Congruency
Use the given property to complete each statement.
1.  Symmetric Property of Equality If MN = UT, then ?.
2.  Division Property of Equality If 4m∠QWR = 120, then ?.
3.  Transitive Property of Equality If SB = VT and VT = MN, then ?.
4.  Addition Property of Equality If y - 15 = 36, then ?.
5.  Reflexive Property of Congruence JL≅ ?
Name the property that justifies each statement.
6.  If m∠G = 35 and m∠S = 35, then m∠G ≅ m∠S.
7.  If 10x + 6y = 14 and x = 2y, then 10(2y) + 6y = 14.
8.  If TR = MN and MN = VW, then TR = VW.
9.  If JK≅LM, then LM≅JK.
10.  If ∠Q ≅ ∠S and ∠S ≅ ∠P, then ∠Q ≅ ∠P.
Give a reason for each step.
11.
12.
Fill in the missing information. Solve for x and justify each step.
13.
14.
REVIEW: ∠RWS = 9x + 1, ∠RWT = 4(5x – 1), ∠QWT = 136°
1. Find the value of x.
2. Find m∠RWS
R
S
Q
3. Find m∠SWT
4. Find m∠RWT
5. Find m∠QWR
W
T
Section 2.4: Inverses and Contrapositives
Write the negation of each statement.
1.  The angle measure is 65.
2.  Tina has her driver’s license.
3.  The figure has eight sides.
4.  The restaurant is not open on Sunday.
5.  ∆ABC is not congruent to ∆XYZ.
6.  m∠Y > 50
Write (a) the inverse and (b) the contrapositive of each statement. Give the truth value of each.
7.  If two triangles are congruent, then their corresponding angles are congruent.
8.  If you live in Toronto, then you live in Canada.
Write the converse, inverse, and contrapositive for each conditional.
9.  If you live in Atlantis, then you need a snorkel.
10.  If the moon is full, then the owls are out.
11.  Two lines intersect at exactly one point.
12.  If you see spots in front of your eyes, then you are looking at a leopard.
REVIEW:
T
U
7x + 3
S
V
8x - 8
W
1. 
2. 
3. 
4. 
5. 
Solve for x
Find m∠TVS
Find m∠UVW
Find m∠TVU
Find m∠SVW
Section 2.5: Proving Angles Congruent
Identify the two statements that contradict each other.
2. I. AB ≅ AC
1.  I. AB and AC are opposite rays
II. ∠B is obtuse
II. ∠CAB is a straight angle
III. ∆ABC is isosceles III. Points A, B, and C define a plane
3. I. AB ≅ CD
II. AB ⟂ CD
III. AB ∥ CD
Find the values of the variables.
4.
5.
6.
7.
8.
9.
Write three conclusions that can be drawn from each figure.
10.
11.
12.
13. Given PQ ≅ QS and QS ≅ ST, PROVE PQ = ST.
REVIEW: Draw each of the following triangles. Write “impossible” if you cannot.
1. Isosceles acute
2. Right scalene
3. Isosceles obtuse
4. Right isosceles
Unit 2 Review
Write the converse, inverse, and the contrapositive of each statement.
1.  If two angles are vertical, then they are congruent.
2.  If figures are similar, then their side lengths are proportional.
3.  If a car is blue, then it has no doors.
Write a conditional for each statement and if possible a biconditional.
4.  A quadrilateral has four sides.
5. The sum of the angles in a triangle is 180°.
Write the negation of each statement.
6.  Two angles are congruent.
7. The angle is not right.
8. The figure is a triangle.
Identify the two statements that contradict each other.
9.  I. ∆PQR is equilateral.
10. I. Line r and m are skew.
II. ∆PQR is a right triangle.
II. Line r and m do not intersect.
III. ∆PQR is isosceles.
III. r∥m
11. I. Each of the two items that Val bought costs more than $10.
II. Val spent $34 for the two items.
III. Neither of the two items that Val bought costs more than $15.
Choose the correct vocabulary term to complete each sentence.
12.  To write a(n) (indirect proof, negation) , you start by assuming that the opposite of what you want to
prove is true.
13.  In a conditional statement, the part that directly follows if is the _________________________.
14.  If “a=b, and b=c, then a=c” is an example of the ____________________ property of congruency.
15.  When a conditional and its converse are true, they may be written as a single true statement called a
_____________________________.
16.  The _______________ of a conditional switches the hypothesis and the conclusion.
17.  The part of a conditional statement that follows “then” is the ________.
18.  The _______________ of a statement has the opposite truth value.
19.  A(n)___________________ is the negation and interchanging of the hypothesis and conclusion.
20.  Reasoning logically from given statements to form a conclusion is _______________________.
21.  A statement that you prove true is a ________________.
Find the value of each variable and all angle measures.
22.
23.
24.
25.
27.
26.