## Lesson 21 Conditional Statements

**Monitoring Progress**

Use red to identify the hypothesis and blue to identify the conclusion. Then rewrite the conditional statement in if-then form.

Question 1.All 30° angles are acute angles.Answer: If an angle measures 30°, then it is acute angle.

Question 2.2x + 7 = 1. because x = 3.Answer: If x = -3, then 2x + 7 = 1

In Exercises 3 and 4, write the negation of the statement.

Question 3.Answer: The shirt is not green

Question 4.The Shoes are not red.Answer: The shoes are red

Question 5.Repeat Example 3. Let p be the stars are visible and let q be it is night.Answer:p q If the stars are visbile, then it is night Trueq p If it is night, then the stars are visible Falsep q If the stars are not visbile, then it is not night Falseq p If it is not night, then the stars are not visible True

Use the diagram. Decide whether the statement is true. Explain your answer using the definitions you have learned.

Question 6.JMF and FMG are supplementary.Answer: True. They are a linear pair

Question 7.Point M is the midpoint of \.Answer: False. There is mo marking to show \ \

Question 8.JMF and HMG arc vertical angles.Answer: True. They share a vertex and their sides for, opposite rays.

Question 9.Answer: False. You cannot assume their intersection is a right angle without markings.

Question 14.Make a truth table for the conditional statement p ~ q.Answer:

**Vocabulary and Core Concept Check**

Question 3.If a polygon is a pentagon, then it has five sides.Answer:

## Reasoning And Proofs Chapter Review

#### 2.1 Conditional Statements

Write the if-then form, the converse, the inverse, the contrapositive. and the biconditional of the conditional statement.

Question 1.Two lines intersect in a Point.

Question 2.4x + 9 = 21 because x = 3.Answer:

Supplementary angles sum to 180°.Answer:

#### 2.2 Inductive and Deductive Reasoning

Question 5conclusion can you make about the difference of any two odd integers?Answer:

What conclusion can you make about the product of an even and an odd integer?Answer:

Question 7.Use the Law of Detachment to make a valid conclusion.If an angle is a right angle, then the angle measures 90°. B is a right angle.Answer:

Question 8.Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements: If x = 3, then 2x = 6. If 4x = 12. then x = 3.Answer:

Use the diagram at the right to determine whether you can assume the statement.

Question 9.Points A, B, C, and E are coplanar.Answer:

3 19x 15Answer:

Write the if-then form, the converse, the inverse, the contrapositive. and the biconditional of the conditional statement.

Question 10.Two planes intersect at a line.Answer:

A relation that pairs each input with exactly one output is a function.Answer:

Use inductive reasoning to make a conjecture about the given quantity. Then use deductive reasoning to sIm that the conjecture is true.

Question 12.the sum of three odd integersAnswer:

the product of three even integersAnswer:

You visit the zoo and notice the following

## Glencoe Geometry Chapter 1 Test Form 2a Answer Key

Transcript Glencoe geometry chapter 1 test form 2a answer key. DATE 2 Chapter 2 Test, Form 2D SCORE 1. Make a conjecture about the next term in this sequence: 5, -10, 20, -40. If mA = mB, then A B. 20. Bonus If the ratio of m1 to m2 is 5 to 4, find m2 Glencoe geometry chapter 1 test form 2a answer key.

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## Performance Task: Induction And The Next Dimension

Mathematical Practices

Explain the purpose of justifying each step in Exercises 5-14 on page 96.Answer:

Create a diagram to model each statement in Exercises 5-10 on page 103.Answer:

Question 3.Explain why you would not be able to prove the statement in Exercise 21 on page 113 if you were provided with the given information or able to use an postulates or theorems.Answer:

## Study Skills: Using The Features Of Your Textbook To Prepare For Quizzes And Tests

**Mathematical Practices**

Question 1.Provide a counter example for each false conditional statement in Exercises 17 24 on page 71.

Question 2.Create a truth table for each of your answers to Exercise 59 on page 74.Answer:

Question 3.For Exercise 32 on page 88. write a question you would ask your friend about his or her interpretation.Answer:

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## Big Ideas Math Book Geometry Answer Key Chapter 2 Reasoning And Proofs

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Some rectangles are not squares.Therefore, some squares are not trapezoids.Answer:

If polygon ABCD is a square. then ills a rectangle.Polygon ABCD is a rectangle.Therefore, polygon ABCD is a square.Answer:

If polygon ABCD is a square, then it is a rectangle.Polygon ABCD is not a square.Therefore, polygon ABCD is not a rectangle.Answer:

**Exploration 1**

Determining Whether a Statement is True or False

Work with a partner: A hypothesis can either be true or false. The same is true of a conclusion. For a conditional statement to be true, the hypothesis and conclusion do not necessarily both have to be true. Determine whether each conditional statement is true or false. Justify your answer.

a. If yesterday was Wednesday, then today is Thursday.Answer:

b. If an angle is acute. then it has a measure of 30°.Answer:

c. If a month has 30 days. then it is June.Answer:

**Exploration 2**

**Exploration 3**

## Lesson 23 Postulates And Diagrams

**Monitoring progress**

Question 1.Use the diagram in Example 2. Which postulate allows you to say that the intersection of plane P and plane Q is a line?Answer:

Use the diagram in Example 2 to write an example of the postulate.a. Two Point Postulate

H, F, and D are coplanar. Plane T plane S. Point B bisects \. ABH and HBF are a linear pair.

Question 24.**HOW DO YOU SEE IT?**Use the diagram of line m and point C. Make a conjecture about how many planes can be drawn so that line m and point C lie in the same plane. Use postulates too justify your conjecture.Answer:

Question 25.**MATHEMATICAL CONNECTIONS**One way to graph a linear equation is to plot two points whose coordinates satisfy the equation and then connect them with a line. Which postulate guarantees this process works for any linear equation?Answer:

Question 26.**MATHEMATICAL CONNECTIONS**A way to solve a system of two linear equations that intersect is to graph the lines and find the coordinates of their intersection. Which postulate guarantees this process works for an two linear equations?Answer:

In Exercises 27 and 28, rewrite the postulate in if-then form. Then write the converse, inverse, and contrapositive and state which ones are true.

Question 27.Two Point Postulate Answer:

Question 31.**MAKING AN ARGUMENT**Your friend claims that even though two planes intersect in a line, it is possible for three planes to intersect in a point. Is your friend correct? Explain your reasoning.Answer:

Question 35.

\ = 5Answer:

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## Reasoning And Proofs Cumulative Assessment

Question 1.Use the diagram to write an example of each postulate.a. Two Point Postulate : Through any two points, there exists exactly one line.Answer:

b. Line Intersection Postulate : If two lines intersect, then their intersection is exactly one point.Answer:

c. Three Point Postulate : Through any three noncollinear points, there exists exactly one plane.Answer:

d. Plane-Line Postulate : If two points lie in a plane, then the line containing them lies in the plane.Answer:

e. Plane Intersection Postulate : If two planes intersect, then their intersection is a lineAnswer:

Enter the reasons in the correct positions to complete the two-column proof.Answer:

Classify each related conditional statement. based on the conditional statementIf I study, then I will pass the final exam.a. I will pass the final exam if and only if I study.Answer:

b. If I do not study, then I will not pass the final exam.Answer:

c. If I pass the final exam, then I studied.Answer:

d. If I do not pass the final exam, then I did not study.Answer:

List all segment bisectors given x = 3.Answer:

Question 5.You are given mFHE = mBHG = mAHF = 90°. Choose the symbol that makes each statement true. State which theorem or postulate. if any, supports your answer.

=

b. m4 ______ m7Answer:

c. mFHE _______ mAHGAnswer:

d. mAHG + mGHE _______180°Answer:

Find the distance between each pair of points. Then order each linesegment from longest to shortest.a. A, BAnswer:

b. C, DAnswer:

c. E, FAnswer:

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## Inductive And Deductive Reasoning

**Exploration 1**

Writing a Conjecture

Work with a partner: Write a conjecture about the pattern. Then use your conjecture to draw the 10th object in the pattern.a.The circle is rotating from one vertex to the next in a clockwise direction

b.Answer:The pattern alternates between a curve in an odd quadrant and a line with a negative slope in the even quadrant.

c.The pattern alternates between the first three arrangements, then their respective mirror images.

**Exploration 2**

Using a Venn Diagram

Work with a partner: Use the Venn diagram to determine whether the statement is true or false. Justify your answer. Assume that no region of the Venn diagram is empty.

**CONSTRUCTING VIABLE ARGUMENTS**To be proficient in math, you need to justify your conclusions and communicate them to others.

a. If an item has Property B. then it has Property A.Answer:

b. If an item has Property A. then it has Property B.Answer:

c. If an item has Property A, then it has Property C.Answer:

d. Some items that have Property A do not have Property B.Answer:

e. If an item has Property C. then it does not have Property B.Answer:

f. Sonic items have both Properties A and C.Answer:

g. Some items have both Properties B and C.Answer:

**Exploration 3**

Reasoning and Venn Diagrams

Answer:

Question 4.Make and test a conjecture about the sign o1 the product of any three negative integers.Answer:

Make and test a conjecture about the sum of any five consecutive integers.Answer:

## Exercise 25 Proving Statements About Segments And Angles

Vocabulary and Core Concept Check

Question 1.How is a theorem different from a postulate?Answer:A postulate is a rule that is accepted to be true without proof and a theorem is a statement that can be proven by using definitions, postulates, and previously proven theorems.

Question 2.**COMPLETE THE SENTENCE**In a two-column proof, each __________ is on the left and each __________ is on the right.Answer: In a two-column proof, each statement is on the left and each reason is on the right.

Monitoring Progress and Modeling with Mathematics

In Exercises 3 and 4. copy and complete the proof.

Question 3.

Answer: Reflexive Property of Angle Congruence

Question 7.If G H. then H G.Answer:

Question 8.\Answer: The statement is talking about reflexity involving line segments, we can say that this observes the Reflexive Property of Segment Congruence

Question 9.If \, then \.Answer:

Question 10.If L M and M N, then L N.Answer: Since the if-then statement is talking about transitivity involving angles, we can say that this observes the Transitive Property of Angle Congruence

PROOFIn Exercises 11 and 12, write a two-column proof for the property.

Question 11.Reflexive Property of Segment Congruence Answer:

Transitive Property of Angle Congruence Answer:

From AB = BC and AB = FG substitution property of equalityBC = FGFrom BC = FG and DF = FG substitution property of equality\ \

Question 19.Explain why you do not use inductive reasoning when writing a proof.Answer:

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## Exercise 22 Inductive And Deductive Reasoning

**Vocabulary and Core Concept Check**

Question 1.How does the prefix counter help you understand the term counterexample?Answer:

In Exercises 9 12. make and test a conjecture about the given quantity.

Question 9.the product of any two even integersAnswer:

the sum of an even integer and an odd integerAnswer:

the quotient of a number and its reciprocalAnswer:

the quotient of two negative integersAnswer:

In Exercises 13 16, find a counter example to show that the conjecture is false.

Question 13.The product of two positive numbers is always greater than either number,Answer:

Question 14.If n is a nonzero integer, then \ is always greater than 1.Answer:

Question 15.If two angles are supplements of each other. then one of the angles must be acute.Answer:

Question 16.A line s divides \ into two line segments. So, the lines is a segment bisector of \Answer:

In Exercises 17 20. use the Law of Detachment to determine what you can conclude from the given information, if possible.

Question 17.If you pass the final, then you pass the class. You passed the final.Answer:

Question 18.If your parents let you borrow the ear, then you will go to the movies with your friend. you will go to the movies with your friend.Answer:

Question 19.If a quadrilateral is a square. then it has four right angles. Quadrilateral QRST has four right angles.Answer:

In Exercises 21 24, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible.

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## Big Ideas Math Geometry Answers Chapter 2 Reasoning And Proofs

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## Reasoning And Proofs Mathematical Practices

**Monitoring Progress**

Question 1.Figure ABC is a triangle.Therefore, figure ABC is a polygon.Answer:Yes, all the triangles are examples of polygons the name itself tells how many sides the shape has.Thus all the triangles are polygons.

Question 2.Some rectangles are not squares.Therefore, some squares are not trapezoids.Answer:No, all the squares are not trapezoids.A trapezoid is a quadrilateral with at least one pair of parallel sides.In square there are always two pairs of parallel sides.

Question 3.If polygon ABCD is a square. then ills a rectangle.Polygon ABCD is a rectangle.Therefore, polygon ABCD is a square.Answer:Yes, Polygon ABCD is a square.

Question 4.If polygon ABCD is a square, then it is a rectangle.Polygon ABCD is not a square.Therefore, polygon ABCD is not a rectangle.Answer:No, Polygon ABCD is not a rectangle.Polygons are plane figures made up of line segment.

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## Chapter 3 Test Form 2b Answers Geometry

3 Chapter 3 Test, Form 2C DATE PERIOD SCORE sv qq 6/3 For Questions 1 and 2, refer to the figure. 1. Identify the intersection of plane SVX and plane STU. 2. Name a segment skew to WY. For Questions 35, identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 3. L 2 and L 12 4.

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## Exercise 26 Proving Geometric Relationships

Vocabulary and Core Concept Check

Question 1.Explain why all right angles are congruent.Answer:All the right angles have a measure of 90°, and angles with the same measure are congruent.

Question 2.What are the two types of angles that are formed by intersecting lines?Answer:Angles formed by intersecting lines are vertical angles and supplementary angles.

Monitoring Progress and Modeling with Mathematics

In Exercises 3-6. identify the pairs) of congruent angles in the figures. Explain how you know they are congruent.

Question 3.

Question 19.**PROVING A THEOREM**Copy and complete the paragraph proof be the Congruent Complements Theorem . Then write a two-column proof.Given 1 and 2 are complementary1 and 3 are complementaryProve 2 31 and 2 are complementary, and 1 and 3 are complementary. By the definitionof ____________ angles. m1 + m2 = 90° and ____________ = 90°. By the ____________ m1 + m2 = m1 + m3. By the Subtraction ____________Property of Equality, ____________ . So. 2 3 by the definition of ____________ .Answer:

Question 20.**PROVING A THEOREM**Copy and complete the two column proof for the Congruent Supplement Theorem . Then write a paragraph proof. Given 1 and 2 are supplementary3 and 4 are supplementary1 and 4

mM = mJ = 90°mK = mL = 90°\ \, \ \

Question 27.**CRITICAL THINKING**Is the converse of the Linear Pair Postulate true? If so, write a biconditional statement. Explain your reasoning.Answer: