Formal Geometry Chapter 2 Homefun Answers

Day 2.1

Unit 2 – Day 2 –Conditional Statements Worksheet

Underline the hypothesis, and circle the conclusion of each conditional statement.

1. If you eat breakfast, then you will feel better at school.

2. If two lines are perpendicular, then they form right angles.

3. If two angles are supplementary, then their sum is 180 degrees.

4. If a nonzero number has exactly two factors, then the number is prime. Write each statement in if-then form.

5. All students at Reno High School take an English class. If you are a student at Reno High School, then you take an English class.

6. All right angles measure 90 degrees.

If an angle is a right angle, then it measures 90 degrees.

7. Every dog has four legs.

If it is a dog, then it has four legs.

8. All vertical Angles are congruent.

If it is a Vertical Angle, then it is congruent.

9. All cats chase mice.

If it is a cat, then it chases mice.

10. Given the Conditional Statement, “If there is fresh snow on the mountains, then it is a good day for snowboarding.” Find the following. Hypothesis: there is fresh snow on the mountains Conclusion: it is a good day for snowboarding Inverse: If there is not fresh snow on the mountains, then it not is a good day for snowboarding Converse: If it is a good day for snowboarding, then there is fresh snow on the mountains. Contrapositive: If it not is a good day for snowboarding, then there is not fresh snow on the mountains. Biconditional: There is fresh snow on the mountains if, and only if it is a good day for snowboarding.

11. Given the Conditional Statement, “If I go to the RHS soccer game, then I have school spirit.” Find the following. Hypothesis: I go to the RHS soccer game Conclusion: I have school spirit. Inverse: If I do not go to the RHS soccer game, then I don’t have school spirit. Converse: If I have school spirit, then I got to the RHS Soccer game Contrapositive: I do not have school spirit, then I do not go to the RHS soccer game. Biconditional: I go to the RHS soccer game if and only if I have school spirit. 12. Given the conditional statement, “If two angels form a linear pair, then they are not complementary.” Find the following. Hypothesis: two angels form a linear pair, Conclusion: then they are not complementary.” Inverse: If they are not complementary, then two angles form a linear pair. Converse: If two angles are not complementary, then they form a linear pair.

Contrapositive: If two angles are complementary, then they do not form a linear pair. Biconditional: Two angles form a linear pair if and only if they are not complementary.

13. What is the inverse and the truth value of the inverse of the following conditional statement?

If an angle is a right angle, then its measure is 90 degrees.

a) If an angle is not a right angle, then it measure is 90 degrees. False Statement

b) If an angle is not a right angle, then it measure is 90 degrees. True Statement

c) If an angle is not a right angle, then its measure is not 90 degrees. True Statement

d) If an angle is not a right angle, then its measure is not 90 degrees. False Statement

14. Which of the following is logically equivalent to the following statement?

If you are a single man, then you are a bachelor.

a) If you are a bachelor, then you are a single man.

b) If you are not a bachelor, then you are not single man.

c) If you are not a single man, then you are not a bachelor.

d) If you are a bachelor, then you are not a single man.

Mixed Review:

15. Points, J, K, and L are district points that 𝐽𝐾 = 𝐾𝐿. Which of the following must be true? Select all that apply

a) 𝐽, 𝐾, 𝑎𝑛𝑑 𝐿 are coplanar b) 𝐽, 𝐾, 𝑎𝑛𝑑 𝐿 are collinear c) K is the midpoint of 𝐽�̅�.

d) 𝐽𝐾̅̅ ̅ ≅ 𝐾𝐿̅̅ ̅̅ e) 𝑚∠𝐽𝐾𝐿 = 90° f) ∠𝐽𝐾𝐿 is a straight angle.

16. Find the approximate perimeter and area of the triangle with vertices (3, 2), ( 2, 2)R S and

(3,4).T

2

11 61

15

P units

A units

Day 2.3

Invalid

Valid

Invalid

Valid

No Conclusion

If Tina has a GPA of 3.0

then she will have her name

in the school paper

No Conclusion

If the measure of an

is between 90 & 180,

then it is not acute

Day 2.4 – Part I

16. Intersecting Lines Postulate

17. Intersecting Planes Postulate

18. Three Non-Collinear Points Postulate

19. Lines on Planes Postulate

20. Two Points Make a Line Postulate

21. Three Non-Collinear Points Postulate

22. Lines on Planes Postulate

23. Intersecting Lines Postulate

AlwaysNever

Sometimes

Always

Never

Sometimes

Name: _____________________________ Date: ____________________ Period:____________

Unit 2 – Proofs – Day 2.4.2 – Algebra Proofs

Name the property used to make the conclusion.

1. If 𝑥 + 7 = 23, then 𝑥 = 16. 1. _Subtraction Prop of =

2. If 𝑥 − 12 = −10, 𝑡ℎ𝑒𝑛 𝑥 = 2. 2. ___Addition Prop of =

3. If 4𝑥 = 40, then 𝑥 = 10 3. _Division Prop of =

4. If 𝑥

3= 12, then 𝑥 = 36. 4. _Multiplication Prop of =

5. If you have 3𝑥 + 12𝑥, then you have 15𝑥. 5. __Math Fact_______

6. if 𝑥(2 + 𝑦), the 2𝑥 + 𝑥𝑦. 6. ___Distributive Prop_

Complete the following Algebra proofs give a reason for each step.

7. Given: 5 2 1 9 2x x

Prove: 7x

Statements Reasons

1) 5 2 1 9 2x x 1) Given

2) 10 5 9 2x x 2) Distributive Prop

3) 10 9 7x x 3) Addition Prop of =

4) 7x 4) Subtraction Prop of =

8. Given: 8 5 2 15x x

Prove: 1x

Statements Reasons

1) 8 5 2 15x x 1) Given

2) 10 5 15x 2) Addition Prop of =

3) 10 10x 3) Addition Prop of =

4) 1x 4) Division Prop of =

9. Given: 6 3 9 1x x

Prove: 4x

Statements Reasons

1) 6 3 9 1x x 1) Given

2) 6 3 9 9x x 2) Distributive Prop

3) 6 12 9x x 3) Addition Prop of =

4) 12 3x 4) Subtraction Prop of =

5) 4 x 5) Division Prop of =

6) 4x 6) Symmetric

10. Given: 10 3 3 2 4x x VARIOUS ANSWERS

Prove: 2x

Statements Reasons

1) 10 3 3 2 4x x 1) Given

2) 10 3 3 6 4x x 2) Distributive Prop

3) 10 3 3 2x x 3) Math Fact

4) 10 6 2x 4) Addition Prop of =

5) 12 6x 5) Addition Prop of =

6) 2 x 6) Division Prop of =

7) 2x 7) Symmetric Property

11. Given: 55 3(9 12) 64x x VARIOUS ANSWERS

Prove: 1x

Statements Reasons

1) 55 3(9 12) 64x x 1) Given

2) 55 27 36 64x x 2) Distributive Prop

3) 28 36 64x 3) Math Fact

4) 28 28x 4) Addition Prop of =

5) 1x 5) Division Prop of =

12. Given: 𝑚 = 𝑛 + 5

2𝑚 = 𝑛

Prove: 𝑚 = −5

Statements Reasons

1) 𝑚 = 𝑛 + 5 1) Given

2) 2𝑚 = 𝑛 2) Given

3) 𝑚 = 2𝑚 + 5 3) Substitution

4) − 𝑚 = 5 4) Subtraction Prop of =

5) 𝑚 = −5 5) Division Prop of =

13. Given: 𝑔 = 2ℎ, 𝑔 + ℎ = 𝑘, 𝑘 = 𝑚

Prove: 𝒎 = 𝟑𝒉

Statements Reasons

1) 𝑔 = 2ℎ 1) Given

2) 𝑔 + ℎ = 𝑘 2) Given

3) 𝑘 = 𝑚 3) Given

4) 2ℎ + ℎ = 𝑘 4) Substitution

5) 3ℎ = 𝑘 5) Math Fact

6) 3ℎ = 𝑚 6) Substitution

7) 𝑚 = 3ℎ 7) Symmetric Property

Unit 2 – Proofs – Day 2.4.2 – Algebraic Proofs Examples 1-4: Write a 2 column proof

1. Given: 5 1

38

x

Prove: 5x

2. If AB AC

Then 4x

3. If Y Z Then 100x

4. If MPN QPN

Then 16x

Mixed Review: