Name:________________________ Date: ________ Time:____________

Unit 2 – Day 2.2 –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.

6. All right angles measure 90 degrees.

7. Every dog has four legs.

8. All vertical Angles are congruent.

9. All cats chase 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: Conclusion: Inverse: Converse:

Contrapositive: Biconditional: 11. Given the Conditional Statement, “If I go to the RHS soccer game, then I have school spirit.” Find the following. Hypothesis: Conclusion: Inverse: Converse: Contrapositive: Biconditional:

12. Given the conditional statement, “If two angels form a linear pair, then they are not complementary.” Find the following. Hypothesis: Conclusion: Inverse: Converse: Contrapositive: Biconditional: 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

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. ____________________________

2. If 𝑥 − 12 = −10, 𝑡ℎ𝑒𝑛 𝑥 = 2. 2. ____________________________

3. If 4𝑥 = 40, then 𝑥 = 10 3. ____________________________

4. If 𝑥

3= 12, then 𝑥 = 36. 4. ____________________________

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

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

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)

3) 10 9 7x x 3)

4) 7x 4)

8. Given: 8 5 2 15x x

Prove: 1x

Statements Reasons

1) 8 5 2 15x x 1) Given

2) 10 5 15x 2)

3) 10 10x 3)

4) 1x 4)

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)

3) 6 12 9x x 3)

4) 12 3x 4)

5) 4 x 5)

6) 4x 6)

10. Given: 10 3 3 2 4x x

Prove: 2x

Statements Reasons

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

Prove: 1x

Statements Reasons

12. Given: 𝑚 = 𝑛 + 5

2𝑚 = 𝑛 Prove: 𝒎 = −𝟓

Statements Reasons

13. Given: 𝑔 = 2ℎ, 𝑔 + ℎ = 𝑘, 𝑘 = 𝑚

Prove: 𝒎 = 𝟑𝒉

Statements Reasons

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: 5. Write the following conditional statement in the following forms.

Conditional Statement: If two angles are complementary, then those two angles are not supplementary.

a) Inverse:

b) Converse:

c) Contrapositive:

d) Biconditional:

6. Given the following: which angle(s) are congruent to ∠𝐺 ?

∠𝐵 is a complement of ∠𝐴

∠𝐶 is a supplement of ∠𝐵 ∠𝐷 is a supplement of ∠𝐶 ∠𝐸 is a complement of ∠𝐷 ∠𝐹 is a complement of ∠𝐸

∠𝐺 is a supplement of ∠𝐹 7. Which of the following are logically equivalent?

A. A conditional statement and its converse

B. A conditional statement and its inverse

C. A conditional statement and its contrapositive

D. A conditional statement, its converse, its inverse and its contrapositive

KEEP GOING….

8. The ratio of <1 to <2 is 2:7. 9. 𝑚∠6 = x2

Find 𝑚 < 1 and 𝑚 < 2. 𝑚∠7 = 5𝑥 + 24

Find x and 𝑚 < 7.

10. The measure of ∠𝐹 is 27° and ∠𝐺 is complementary to ∠𝐹. <G is complementary to <E. Find the 𝑚 < 𝐸.

11. 𝑚∠4 = 𝑥 12. ∠9 𝑎𝑛𝑑 ∠10 𝑎𝑟𝑒 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦. 𝑚∠5 = 𝑥 − 6 <8 and <10 are complementary. 𝑚∠8 = 25.

Find x and m<5. Find m<9 and m<10.

13. Given: ∠𝑌 is supp to ∠𝑋, and ∠𝑍 is supp to ∠𝑋. If ∠𝑌 = 42°, find the complement of ∠𝑍.

14. If 𝐴𝐵 ̅̅ ̅̅ ̅ ⊥ 𝐵𝐶 ̅̅ ̅̅ ̅ , <1 = (4x + 8)o

𝑚∠2 = (6x + 2)o, then find the measure of 𝑚∠3.

Worksheet: Section 2.5.1 – Segment Proofs Part I Examples 1-3: Write a 2 column proof

1. Given: WX YZ

Prove: WY XZ

2. If VZ VY

WY XZ

Then VW VX

3. Given: AC BD

EC ED

Prove: AE BE

Mixed Review: 4. Find 𝑥 if and 𝐴𝐵 if 𝐵 is between 𝐴 and 𝐶, 𝐴𝐵 = 3𝑥, 𝐵𝐶 = 14 and 𝐴𝐶 = 41.

5. Find 𝑃 on 𝑀𝑁 if 𝑃 is 1

3 the distance from 𝑀(−3, −4) to 𝑁(6, 11).

6. Find 𝑚∠𝐴𝐵𝐶 in the figure at the right.

y

x

Worksheet: Section 2.5.2 – Segment Proofs Part II Examples 1-4: Write a 2 column proof 1. Given:

Prove: AC CD

2. If SC HR

HR AB

Then SC AB

is the midpoint of

is the midpoint of

C AE

C BD

AE BD

3. Given: is the midpoint of E DF

CD FG

Prove: CE EG

4. Given: LM PN

XM XN

Prove: LX PX

Worksheet: Section 2.6.1 Angle Proofs Part I Examples 1-3: Find the measure of each numbered angle.

1.

2 comp 3

1 4

m 2=28

2.

2 supp 4

4 supp 5

4=105m

3. 9 3 12

10 24

m x

m x

Examples 4-7: Write a 2 column proof 4.

:

:

Given 4 6

Prove 5 supp to 6

5 64

5.

6.

7.

:

:

Given 4 supp 6

5 supp 7

4 5

Prove 6 7

4 6 75

:

:

Given 6 7

Prove 5 8

86 75

Y

ESOR

Given ABE DBC

Prove 1 3

:

:

23

1

C

ED

B

A

Worksheet: Section 2.6.2 – Angle Proofs Part II Examples 1-3: Find the measure of each numbered angle.

1. 3 2 23

4 5 112

m x

m x

2.

6 2 21

7 3 34

m x

m x

3.

4 3( 1)

5 7

m x

m x

Examples 4-8: Write a 2 column proof

4. 𝐶𝐷 ⃡ ⊥ 𝐷𝐸 ⃡ :Prove comp CDF FDE

C

DE

F

5.

:

:

Given 4 6

Prove 5 6

:Given

4

6

5

6.

7. :Given 𝐶𝐷 ⃡ bisects CBE

: 1 2Prove

8.

1 3

4 2

: 1 4

Given: comp

comp

Prove

:

:

Given 1 4

Prove 2 3

1

32

4

1

3

2

B

E

D

CA

F

G

13

2M

J

H

K

G

4