Find the slope of a line that contains the following points

Find the slope of a line that contains the following points:

1. (2, -4), (5, 2) 2. (-1, 3), (-1, -2) Determine whether the lines through the given points are parallel, perpendicular, or neither: 3. Line 1: (8, 12) (7, -5) 4. Line 1: (-1, 4) (3, -4) Line 2: (-9, 3) (8, 2) Line 2: (2, 7) (5, 1) 5. Write the equation (slope-intercept form) of the line passing through the point (1, 4) and parallel to the line y = -4x + 5. 6. Now write the equation of the line passing through the point (1, 4) and perpendicular to the line y = -4x + 5.

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7. Line h passes through (3, 0) and (7, 6). Graph the line

perpendicular to h that passes through the point (2, 5). (You must find slope of line h first!) 8. Find the slope of a line, n, perpendicular to line h and passing through point P. Then name another point that would lie on line n. Find the coordinates of the midpoint of the segment with the given endpoints.

9. R (3, 1) and S (3, 7) 10. V (2, 4) and W (6, 6)

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11. Use the midpoint and distance formula in the following problem.

a. The endpoints of AB are A (3, 2) and B (6, 7). Find the coordinates of the midpoint M. b. What is the length of AB ? Use the given endpoint R and midpoint M of RS to find the coordinates of the endpoint S.

12. R (1, 2) and M (-2, 1) 13) R (4, 2) and M (0, 4) 14. The endpoints of two segments are given: PQ : P (4, 3), Q (–1, 6), RS : R (2, –3), S (–2, 0) a. Find each segment length. (distance formula or Pythagorean Theorem) b. Are the segments congruent?

*Hint: You can use slope to find the other point!

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Name: __________________________ Block: ____ Date: ____________ Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. 1. ∠l and ∠5

2. ∠4 and ∠6

3. ∠16 and ∠10

4. 17 19and∠ ∠ 5. 23 22and∠ ∠ 6. 18 21and∠ ∠ Identify the angle pair type and then solve for x or y. 7. 8. 9. Angle pair name: Angle pair name: Angle pair name:

__________________ __________________ ___________________

__________________ __________________ ___________________

X=_______ x=_______ x=_______

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10. 11. 12. Angle pair name: Angle pair name: Angle pair name:

__________________ __________________ ___________________

__________________ __________________ ___________________

X=_______ x=_______ x=_______

Find m ∠ 1 and m ∠ 2.

13. 14.

15. Find the values of x and y and name the angle relationship.

a) What type of angle pair is 68 4 16?and y° − ___________________ b) What type of angle pair is 68 2 24?and x° − ___________________ c) What type of angle pair is 2 24 4 16?x and y− − _________________

x=______ y=______ 5

Geometry name: _________________________ Transversals and Angle Pairs date: __________________________ For each diagram of the DOTTED angles, circle ALL the names or properties this pair is GUARANTEED to have or circle NONE if that’s the case. 1. vertical angles linear pair adjacent angles none alternate interior alt. exterior consecutive int. corresponding congruent supplementary complementary

2. vertical angles linear pair adjacent angles none alternate interior alt. exterior consecutive int. corresponding congruent supplementary complementary















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Name___________________________________ Date___________________ Is it possible to prove that lines p and q are parallel? If so, state the postulate or theorem you would use.

1. 2. 3.

Find the value of x that makes m ║ n then write the postulate or theorem you used.

4. 5. 6.

7. 8. 9.

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State the angle pair name and find the value of x an y. 10. 11. 12. Angle pair name: Angle pair name: Angle pair name:

__________________ __________________ ___________________

__________________ __________________ ___________________

X=_______ x=_______ x=_______

Y=_______

In Exercises 10–14, use the diagram and the given information to determine if m ║ n, p ║ q, or neither. 10. ∠3 ≅ ∠10

11. ∠1 ≅ ∠13

12. ∠4 ≅ ∠11

13. ∠12 ≅ ∠13

14. ∠3 ≅ ∠14

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16. GIVEN: q || r

PROVE: ∠ 1 ≅ ∠ 3 Statements Reasons

1. q || r

1. ____________________________ 2. ____________________________

2. ∠ 1 ≅ ∠ 2

3. ∠ 2 ≅ ∠ 3 3. ____________________________

4. ∠ 1 ≅ ∠ 3 4. ____________________________

REVIEW 17. Write the definition of parallel lines in biconditional form: Use the Law of Detachment to make a valid conclusion. 18. If the measure of an angle is less than 90°, then the angle is acute. The measure of ∠A is 46°. 19. If a food has less than 140 milligrams of sodium per serving, then it is low sodium. A serving of

soup has 90 milligrams of sodium per serving.

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Name: _____________________ Block: ________ Date: ___________ Find the angle measure. Tell which postulate or theorem you use. 1. If m∠ 4 = 65°, then m∠ 1= _______.

Postulate/Theorem: _____________________

2. If m∠ 7 = 110°, then m∠ 3 = ______. Postulate/Theorem: _____________________



5. If m∠ 8= 54°, then m∠ 1 =_______. Postulate/Theorem: _____________________

Error Analysis: A student concludes that ∠ 9 ≅ ∠ 10 by the Corresponding Angles Postulate. Correct and describe the error in this reasoning. 6. Correction:

Description:

7. PROOF Given: n p Prove: ∠ 1 and ∠ 2 are supplementary Statements Reasons 1. ________________ 1. Given

2. 1 3∠ ≅ ∠ 2. __________________________

3. ________________ 3. Definition of congruent angles

4. 2 3 180m m∠ + ∠ = ° 4. __________________________

5. ________________ 5. Substitution

6. ∠ 1 and ∠ 2 are 6. __________________________

supplementary

n

p

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Can you prove that lines a and b are parallel? If so, explain how. (name the postulate or theorem used)

8. 9. 10.

yes or no yes or no yes or no reason: ________________ reason: ________________ reason: ______________

11. Complete the steps below to determine whether DB

and HF

are parallel.

Step 1: Find m∠DCG and m∠ CGH. Step 2: Describe the relationship between ∠DCG and ∠ CGH. Are DB

and HF

parallel? Explain your reasoning. Use the diagram. How would you show that the given lines are parallel?

12. a and b: 13. b and c:

14. d and f: 15. e and g: 16. a and c: 17. Find the values of x and y.

x = ______

y = ______

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Geometry – Chapter 3 Additional Practice

1. The map at the right shows the downtown area of a city. Name two points of locations that represent each type of angle.

a. Alternate interior angles b. Consecutive interior angle c. Alternate exterior angle d. Corresponding angle

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Name:__________________ Block: ______ Date:__________

#1-4: Use the diagram for the following questions. You must use each of the angles at least once.

1. Write two sets of alternate interior angles.

2. Determine two sets of corresponding angles.

3. What are two sets of consecutive interior angles?

4. Determine two sets of alternate exterior angles. #5- 8: Use the diagram for the following questions.

_______ 5. ∠4 and _____ are corresponding angles.

A ∠7 B ∠5 C ∠3 D ∠8 _______ 6. ∠3 and _____ are consecutive interior angles.

A ∠8 B ∠5 C ∠6 D ∠3 _______ 7. ∠3 and ∠6 are __________ angles.

A consecutive interior B alternate interior C corresponding D vertical

_______ 8. ∠6 and ∠7 are __________ angles. A vertical B consecutive interior C corresponding D alternate interior _______ 9. In the diagram ml , find the _______ 10. In the diagram ml , find the

value of x. value of x.

A 138° A 122° B 128° B 68° C 118° C 58° D 62° D 48°

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#11-14: Answer each question, SHOW ALL WORK, and justify your work by stating the postulate or theorem that allowed you to set up an equation. _______ 11. In the diagram ml , find the value of x.

A 9.5 B 76 C 33 D 10.75

reason:____________________________ _______ 12. In the diagram find the value of x that would make ml .

A 65 B 45 C 22.5 D 60

reason:____________________________

_______ 13. In the diagram ml , find the value of x.

A 35 B 25 C 105 D 125

reason:____________________________

_______ 14. In the diagram find the value of x that would make ml .

A 21 B 24 C 41 D 96

reason:____________________________ #15-18: Short Answer- Show all work and circle your final answer.

15. Find the slope of the line that passes 16. Given that line 1 passes through (-2, 1) through ( ) ( )6,62,2 and− . and (1, -1) and line 2 passes through (1, 3) and (4, 1). Determine if the lines are parallel,

perpendicular, or neither. (Show the slopes of each to get to that conclusion.)

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17. Write the equation of a line in slope-intercept line that is parallel to 𝑦𝑦 = −3𝑥𝑥 + 6 and goes through (3, 7) 18. Write the equation of a line in slope-intercept line that is perpendicular to 𝑦𝑦 = −2𝑥𝑥 − 4 and goes through (−4,− 8) #19 & 20 Find the coordinates of the midpoint & distance of the segment with the given endpoints. 19. A(6, −3) and B(10, 5) 20. A(14, 7) and B(−9, 1) M ( ___, ___ ) M ( ___, ___ )

AB = __________ AB = __________

#21 & 22 Use the given endpoint R and midpoint M of RS to find the coordinates of the other endpoint S.

21. R(8, 0), M(4, −5) 22. R(7, −17), M(−2, 3)

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23. Find the value of x and y. Show your initial equation and work. 24. Is it possible to prove that line c is parallel to line d? _________ How do you know? ________________________

25.) In the diagram, BCAB ⊥ . 26.) Find the measure of the Find the value of x. indicated angles. 1m∠ = ________ 2m∠ = ________ 3m∠ = ________ 4m∠ = ________ 5m∠ = ________ 6m∠ = _______ x = __________

(2x+20)° (3x)°

(5y)°

d

c k

60°

120°

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Find the slope of a line that contains the following points

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