GH Chapter 3 Quiz Review (3.1, 3.2, 3.4, 3.5)

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Name: Class: Date: SHOW ALL WORK GH Chapter 3 Quiz Review (3.1, 3.2, 3.4, 3.5) Match each vocabulary term with its definition. (#1-5) a. parallel lines b. parallel planes c. perpendicular lines d.

1 Name: Class: Date: SHOW ALL WORK GH Chapter 3 Quiz Review (3.1, 3.2, 3.4, 3.5) Match each vocabulary term with its definition. (#1-5) a. parallel lines b. parallel planes c. perpendicular lines d. skew lines e. perpendicular bisector f. perpendicular planes g. angle bisector 1. lines that are not coplanar and do not intersect 2. planes that do not intersect 3. lines in the same plane that do not intersect 4. a line perpendicular to a segment at the segment s midpoint 5. lines that intersect at 90 angles : Writing: Write an equation in slope-intercept form for the graph shown below. What are the slope and vertical intercept of the graph, and what do they tell you about the graph? 9. Identify the transversal and classify the angle pair 11 and :5: Use the information m 1=(3x+ 30), m 2=(5x 10), and x= 20, and the theorems you have learned to show that l Ä m : Write the equation of the line with slope 2 through the point (4, 7) in point-slope form : Write an equation for the line passing through the point Ê Ë Á 3, 5ˆ that has a slope of 5. 1

2 Name: 11. Give an example of corresponding angles : Which lines, if any, can be proved parallel given the following diagram? For each conclusion, provide the justification. 12. Identify a pair of parallel segments : Which lines, if any, must be parallel based on the given diagram and information? Give the justification for each conclusion. Given: 3 is supplementary to A dirt path connects the lanes of a divided highway that runs east-west. An officer in a police car headed east gets a call that requires crossing over to the westbound lanes using the dirt path. 3.5: True or False: 16. If two lines are intersected by a transversal and alternate interior angles are equal in measure, then the lines are parallel. 17. If two lines are intersected by a transversal and corresponding angles are supplementary, then the lines are parallel. Through what angle must the police car turn at the bend in the dirt path? 2

3 Name: : Which pair of lines is parallel if 1 is congruent to 7? 21. Find m 1 in the diagram. (Hint: Draw a line parallel to the given parallel lines.) 19. Find m ABC. 22. Find m 1 in the figure below. PQ and RS are parallel. 20. Find x and y in the diagram. Justify your answer. 23. Multiple Response: Identify all segments skew to FB. Choose all that apply. a. AB b. EH c. AD d. DH e. GC f. CD 3

4 Name: 24. In the figure, 1 and 2 are. 26. Lines a and b in the figure below are parallel. What is the measure of 1, in degrees? : Find the value of x so that mä n : Write a two-column proof. Given: t l, 1 2 Prove: mä l Complete the proof. Proof: 1. [1] 1. Given 2. t m 2. [2] 3. mä l 3. [3] 4

5 Name: : Write a two-column proof. Given: m 1+m 2=180 Prove: l Ä m Complete the proof. Proof: 1. m 1 + m 2 = Given 2. m 1=m 3 2. [1] 3. m 3+m 2= Substitution (Steps 1 and 2) 4. l Ä m 4. [2] Complete this two-column proof. 29. Given: Lines m and n are parallel. Transversal t intersects lines m and n. Prove: m 1 = m 7 1. m Ä n; t intersects m and n 1. Given 2. m 1=m 3; m 5=m m 3=m m 1=m m 1=m

6 GH Chapter 3 Quiz Review (3.1, 3.2, 3.4, 3.5) Answer Section 1. D 2. B 3. A 4. E 5. C 6. y = 3x + 1; The vertical intercept tells where the line crosses the y-axis and the slope tells that the line increases somewhat steeply. 7. y 7=2(x 4) First write the point-slope formula. y y 1 = m(x x 1 ) Then substitute 2 for m, 4 for x 1, and 7 for y 1. y 7=2(x 4) 8. y = 5x The transversal is line l. The angles are corresponding angles. To determine which line is the transversal for a given angle pair, locate the line that connects the vertices. Corresponding angles lie on the same side of the transversal l, on the same sides of lines n and m. 10. By substitution, m 1=3(20)+30= 90 and m 2=5(20) 10= 90. By the Substitution Property of Equality, m 1=m 2= 90. By the Converse of the Alternate Interior Angles Theorem, l Ä m. m 1=3(20)+30= 90 ; Substitute 20 for x. m 2=5(20) 10= 90 m 1 = m 2 = 90 Substitution Property of Equality l Ä m Converse of the Alternate Interior Angles Theorem and 4 Corresponding angles lie on the same side of a transversal, on the same sides of the two lines the transversal crosses. So, 8 and 4 are corresponding angles. 12. AB Ä HG Parallel lines are coplanar and do not intersect. Segments are parallel if the lines that contain them are parallel. Also, parallel lines and segments are indicated by arrows on the drawing b Ä c, Consecutive Interior Angles Converse 15. a Ä b, Consectutive Interior Angles Converse 16. True 17. False 18. c and d 1

7 19. m ABC = 35 (x) = (3x 70) Corresponding Angles Postulate 0 = 2x 70 Subtract x from both sides. 70= 2x Add 70 to both sides. 35= x Divide both sides by 2. m ABC=3x 70 m ABC = 3(35) 70 = 35 Substitute 35 for x. Simplify. 20. x=4; y= m 1 = 135 Step 1 Draw line l parallel to lines m and n. Given: m y+ m z=90, x w, mä n Ä l Step 2 Use the Alternate Interior Angles Theorem to find pairs of congruent angles. y x, z w m y= m x, m z= m w Step 3 Substitute x for y and w for z in the given m y+ m z=90. m x+ m w=90 Step 4 Use the definition of congruent angles and the given x w. m x= m w Step 5 To find m w, substitute w for x. m x+ m w=90 m w+ m w=90 2 m w=90 m w=45 Step 6 Find m 1. 1 and w are supplementary. m 1+m w=180 m 1+45 =180 m 1= B, C, F 24. alternate exterior angles [1] t l, 1 2 [2] 2 intersecting lines form linear pair of s lines. [3] 2 lines to the same line lines Ä. Proof: 1. t l, Given 2. t m 2. If 2 intersecting lines form linear pair of s lines. 3. mä l 3. If 2 lines to the same line lines Ä. 2

8 28. [1] Vertical Angle Theorem [2] Converse of the Same-Side Interior Angles Theorem Proof: 1. m 1 + m 2 = Given 2. m 1=m 3 2. Vertical Angle Theorem 3. m 3+m 2= Substitution (Steps 1 and 2) 4. l Ä m 4. Converse of the Same-Side Interior Angles Theorem NA 1. NA 2. NA 2. Vertical angles are=in measure. 3. NA 3. If 2 lines are intersected by a transversal, then alternate interior angles are = in measure. 4. NA 4. Substitution property (Steps 2 and 3) 5. NA 5. Substitution property (Steps 2 and 4) 3

Geo - CH3 Prctice Test

Geo - CH3 Prctice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the transversal and classify the angle pair 11 and 7. a. The transversal