Angles and Lines Grade 10 (Geometer's Sketchpad, Protractors)

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http://library.thinkquest.org/2647/geometry/angle/angle.htm. Angles and Lines ... guided lessons and worksheets, the students will have the opportunity to make.
Angles and Lines 10th Grade Geometry 5-Day Unit Plan

Tools Used: Geometer’s Sketchpad, Protractors By: Holly Kubicki

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Objectives for the unit: Students must be able to: • Recognize, define and discuss complimentary angles, supplementary angles, right angles, vertical angles, angle bisector, intersecting lines, perpendicular lines, oblique lines, parallel lines and transversals • Draw and measure angles using a protractor • Practice drawing and measuring angles and lines by using Geometer’s Sketchpad • Discover relationships among the angles formed by intersecting lines, perpendicular lines and two parallel lines cut by a transversal • Observe and locate interior angles and exterior angles • Locate and explain why same side interior angles are supplementary • Locate and explain why alternate interior angles, alternate exterior angles, corresponding and vertical angles are congruent NCTM Standards for Grades 9-12: Geometry Standard Measurement Standard Communication Standard New York State Standards MST Standard 3 Key Idea 4- Modeling/Multiple Representation Key Idea 5-Measurement Resources TextbookD.C. Heath and Company, Geometry: An Integrated Approach, Roland E. Larson, Laurie Boswell, Lee Stiff, Chapter 2&3: pg. 71,90-91,101,105,134-140, Copyright 1998 Web Site-

http://library.thinkquest.org/2647/geometry/angle/angle.htm Angles and Lines by ThinkQuest

Computer Applications-

Geometer’s Sketchpad

Materials Computers with Geometer’s Sketchpad Overhead Projector Protractors Rulers Pencils Worksheets

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♦ Unit Overview ♦ This unit is based on students discovering, exploring and understanding the angle relationships formed by lines. Students will be learning the definitions and properties of angles and lines with the assistance of technology and manipulatives. Through teacher guided lessons and worksheets, the students will have the opportunity to make connections and have a solid understanding of the unit. Day 1: Introduction and Review of Terms Students and teacher will fill in and discuss angle and line vocabulary on a graphic organizer. Day 2: Measuring Angles with Protractors and GSP Teacher will demonstrate and show students how to measure and draw angles using a protractor. Students will compete in group games on measuring and drawing angles. Teacher will then introduce GSP and show students how to construct and measure angles. Students will then practice using GSP to construct and measure angles. Day 3: Intersecting Lines and Perpendicular Lines with GSP Students will use GSP to complete a worksheet on discovering relationships among the angles formed by intersecting and perpendicular lines. Day 4: Parallel Lines Cut by a Transversal with GSP Students will use GSP to complete a worksheet on discovering relationships among the angles formed by parallel lines cut by a transversal. Day 5: Review of Definitions and Concepts Students will work in pairs to complete a review worksheet. Teacher and students will go over the review sheet.

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Day 1 Topic: Introduction and review of terms Learning Objectives: Students must be able to recognize, define and discuss complimentary angles, supplementary angles, right angles, vertical angles, angle bisector, intersecting lines, perpendicular lines, oblique lines, parallel lines and transversals. Motivational Transitioning: Relate: Does anyone know any types of lines or angles? Actively involve: Does anyone know how many degrees are in a straight line? What makes an angle? Do you see any angles around the room? Focus: We need to know the vocabulary of angles and lines in order to explain and prove ourselves when discussing angles and lines. Sharing the goals: Today we are going to learn some useful vocabulary about angles and lines. Instructional Presentation: Teaching/Modeling: 1) Pass out graphic organizer worksheets to the students and display the graphic organizer transparency on the overhead projector. 2) The teacher will state that we will go over, discuss and fill in all the vocabulary terms that are on the graphic organizer and draw in the pictures that represent each term. 3) The teacher will state the first vocabulary term, discuss and write the meaning of the word in the definition part of the graphic organizer on the overhead. The teacher will then think aloud and explain his/her thoughts of drawing the illustration of the word in the picture part of the graphic organizer. To aid in the understanding of the first term- complimentary angles, the teacher could draw a circle on the board which has 360 degrees, then break it into 4 equal parts to show how a straight line has 180 degrees and how complimentary angles have 90 degrees. Guided Practice: 1) Students will then get into groups of about three. 2) In their groups, have the students discuss the meaning of the rest of the words and try to come up with an illustration of the word. The teacher will walk around and ask some questions to get the students to communicate their thoughts about the terms. By thinking about and discussing the terms, this will hopefully stir up some previous knowledge. Closure: 1) After the groups have thought about the meaning of the vocabulary, the teacher will have the groups explain what their group thought the words meant. The teacher will fill in the rest of the graphic organizer with the definitions and illustrations while getting input from the students. Independent Practice/Evaluation: Students will be given a worksheet where they will have to answer questions based on the vocabulary.

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Name:____________________________

Vocabulary

Definition

Angle and Line Vocabulary

Picture

complimentary angles

supplementary angles

right angle

vertical angles

angle bisector

intersecting lines

perpendicular lines

oblique lines

parallel lines

transversal

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Name:_________________________ 1) Is ray BD the angle bisector? Why or why not. __________________________________ __________________________________ __________________________________

A m!

A

B

D

=

B

3

°

3

D m!

D

B

C

=

3

°

2

C

2) A

m!

A

B

D

=

5

Are angles ABD and DBC complimentary to each other? Why or why not. __________________________________ __________________________________ __________________________________

°

4

D m!

D

B

B

C

=

3

6

°

C

A

3) A

m!

D

m!

D

B

B

D

E

=

9

1

°

=

8

9

°

A

m!

B

B

C

m!

C

B

=

8

E

=

9

° 9

1

°

C

Are these intersecting lines oblique or perpendicular? Why. __________________________________ __________________________________ __________________________________

E

4)

1

4 2 3 5 6 8 7

9 10 12 11

Name all the sets of supplementary angles. ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ Name all the sets of vertical angles. ______________ ______________ ______________ ______________ ______________ ______________

5) Draw three parallel lines cut by a transversal.

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Name:____Answer Key___________ 1) Is ray BD the angle bisector? Why or why not. Ray BD is not the angle bisector because_ angle ABD is not equal to angle DBC.___ __________________________________

A m!

A

B

D

=

B

3

°

3

D m!

D

B

C

=

3

°

2

C

2) A

m!

A

B

D

=

5

Are angles ABD and DBC complimentary to each other? Why or why not. Angle ABD is complimentary to angle DBC because when added they both equal 90____ degrees._____________________________

°

4

D m!

D

B

B

C

=

3

6

°

C

A

3) A

m!

D

m!

D

B

B

D

E

=

9

1

°

=

8

9

°

A

m!

B

B

C

m!

C

B

=

8

E

=

9

° 9

1

°

C

Are these intersecting lines oblique or perpendicular? Why. These intersecting lines are oblique because angle ABC, ABD, DBE, & CBE are not right angles that is they are not 90 degrees.______

E

4)

1

4 2 3 5 6 8 7

9 10 12 11

Name all the sets of supplementary angles. _angles 1&2____ _angles 3&4____ _angles 1&4_____ _angles 2&3____ _angles 5&6_____ _angles 7&8____ _angles 6&7_____ _angles 5&8____ _angles 9&10____ _angles 11&12__ _angles 10&11___ _angles 9&12___ Name all the sets of vertical angles. _angles 1&3____ _angles 2&4_____ _angles 5&7____ _angles 6&8_____ _angles 9&11___ _angles 10&12___

5) Draw three parallel lines cut by a transversal.

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Day 2 Topic: Measuring and drawing angles with protractors and GSP Learning Objectives: Students must be able to draw and measure angles using a protractor. Students must practice drawing and measuring angles using GSP. Motivational Transitioning: Relate: Does anyone know what a protractor is used for? Actively Involve: Does anyone know how to use a protractor or any other tool that would help measure and draw angles? Focus: We need to know how to use protractors and other tools so we can measure and draw angles. Sharing the Goals: Today we are going to learn how to measure and draw angles using protractors and a computer program, Geometer’s Sketchpad, so we can have a better understanding of the vocabulary we learned yesterday. Instructional Presentation: First part of Lesson: Teaching/Modeling: 1) Pass out protractors to every student. 2) The teacher will question students about the protractors. For example, ask questions such as, How many degrees does the protractor go up to? How do you know this? How many degrees does a circle have? Is the protractor half a circle? These questions should get the students thinking about what they already know. 3) The teacher will have large angles drawn on the overhead projector so the teacher can demonstrate and explain with his/her protractor how to measure an angle so all the students can see. The teacher will then ask students to explain to teacher how to measure the next few angles. 4) The teacher will then demonstrate and explain to students how to draw an angle for a given measurement on the overhead. The teacher will then ask students to explain to teacher how to draw an angle for a given measurement. Guided Practice: 1) Pass out worksheets of angles and blank sheets of paper to students and have them get into groups of 3. 2) Teacher will have students measure the angles for #1 & #2 on the worksheet to get a feel for using the protractor. The teacher will walk around and help students. 3) The students will then draw an angle for measurement on #3 & #4 on the blank sheet of paper. The teacher will continue to walk around to help students who are having difficulty. Closure: 1) The teacher will then have the groups compete to see which group can measure the angle for #5 the fastest and with the correct angle measurement. Every student in the group must measure the angle and make sure each member came up with the same angle measurement, then raise their hands as a group. The teacher will verify

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the angle measurement and determine which group won. This game will continue for #6#10. 2) The groups will compete again to see which group can draw angles for the measurement on #11 the fastest and with the correct angles drawn. Every student in the group must draw the angle for angle for a given measurement and make sure every member of the group has the correct angle drawn, then raise their hands as a group. The teacher will verify the angle measurement and determine which group won. The game will continue for #12-#16. 3) The teacher will also ask questions throughout the lesson pertaining to the vocabulary learned yesterday such as, What would the compliment of this angle be?, Have the students draw the compliment angle, Are these angles supplementary? Second part of lesson: Teaching/Modeling: 1) The teacher will display Geometer’s Sketchpad on an overhead screen and give students an introduction of how to use Geometer’s Sketchpad. The teacher will give students an overview of how to sketch points, lines, rays, segments, label points and so forth. The teacher will also tell students how to highlight, press Esc to unhighlight everything, use edit tab to undo a mistake, use file tab to open a new sketch and some other important things about the program. 2) The teacher will demonstrate and explain how to draw an angle using rays. Then to find an angle measurement, highlight all 3 points in order and use the measure tab to measure angle. Teacher will show students if you move a point the angle measure will change. Guided Practice: 1) The students will practice at their own computers for a few minutes to get a feel for how the program works. 2) The teacher will then have students draw an angle and get the measure of it while talking them through steps. The teacher will be walking around and helping students. The students can then move around the points on their angle to see how the angle measure changes. Closure: 1) Students will open a new sketch and sketch a right angle, and prove it’s a right angle by showing its measure. The teacher will check the students’ sketches. Independent Practice/Evaluation: Students will be given a worksheet where they will use protractors to measure and draw angles, and answer questions based on the vocabulary.

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Name:_________________________

Measuring and Drawing Angles

1)

2)

3) 155°

4) 40°

5)

6)

7)

8)

9)

11) 90°

10)

12) 104°

13) 52°

14) 76°

15) 38°

16) 180°

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Name:__________________________ 1) Give the angle measure for a & b a)

b)

2) Draw angles for a & b a) 33°

b) 161°

3) Are the two angles complimentary? Why or why not. ___________________ ___________________ ___________________ ___________________ ___________________ ___________________ 4) Are the two angles supplementary? Why or why not. __________________ __________________ __________________ __________________ __________________ __________________ 5) Is ray BC the angle bisector? Why or why not.

A

_____________________________ _____________________________ _____________________________ _____________________________

C

B

D 11

Name:____Answer Key__________ 1) Give the angle measure for a & b a) 44°

b) 143°

2) Draw angles for a & b a) 33°

b) 161°

3) Are the two angles complimentary? Why or why not. Yes, the two angles are complimentary because the first angle is 65°__ and the second angle is 35° and both equal___ 90°________________

4) Are the two angles supplementary? Why or why not. No, the two angles are not supplementary___ because the first angle is 96° and the second angle is 86° and both do not equal 180°___ 5) Is ray BC the angle bisector? Why or why not.

A

Yes ray BC is the angle bisector___ because angle ABC is 53° and____ angle CBD is 53°______________ _____________________________

C

B

D 12

Day 3 Topic: Intersecting lines and perpendicular lines with GSP Learning Objectives: Students must discover relationships among the angles formed by intersecting lines and perpendicular lines. Students must locate and explain why vertical angles are congruent. Motivational Transitioning: Relate: Can someone tell me what intersecting lines are? Actively Involve: Are the vertical angles in intersecting lines always congruent? Focus: We are going to further our understanding of intersecting lines to know why vertical angles are congruent. Sharing the Goals: Today we are going to discover why vertical angles are congruent using what we already know about intersecting lines, vertical angles and supplementary angles. Instructional Presentation: Teaching/Modeling: 1) The teacher will display Geometer’s Sketchpad on an overhead screen and give students a review of the program. 2) The teacher will demonstrate and show students how they will discover angle relationships formed by intersecting lines and perpendicular lines through examples of complimentary and supplementary angles. 3) The teacher will construct complimentary angles and show the measure of each angle and the right angle measure as shown below. By moving the ray BD, the students will see the 2 angles will always equal 90˚ A D

B m !A B C = 9 0 ° m !A B D = 4 5 ° m !D B C =

C

4 5

°

4) The teacher will then construct supplementary angles and show the measure of each angle and the straight angle measure as shown below. By moving ray BD, the students will see the angles will always equal 180˚. D

A

C

B m!

ABC

=

1 80

° m !A B D = 1 3 1 ° m! D B C =

4 9

°

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Guided Practice: 1) The teacher will pass out worksheets and have students work at their own computers to complete the worksheet. The students will be able to help each other out and work along with the students sitting next to them. The teacher will also be circulating the room aiding students and asking questions. Closure: 1) The teacher will review the worksheet by asking students for their answers and explanations. Independent Practice/Evaluation: Students will be given a worksheet where they will have to exercise their understandings of intersecting lines, vertical angles and perpendicular lines.

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Name:_____________________

Intersecting and Perpendicular Lines

Directions: Follow instructions and answer questions. 1) GSP: Construct two lines that intersect.

2) GSP: Highlight both lines, go to Construct tab and construct intersection. B

A

3) GSP: Label all 5 points.

E D

C

4) GSP: Find the measure of all 4 angles created by the intersecting lines. What angles are supplementary? _______ & _______, _______ & _______, _______ & _______, _______ & _______ What angles are vertical angles? _______ & _______, _______ & _______ What angles are equal in measure? _______ & _______, _______ & _______ 5) GSP: Move a point on one of the lines, move a point on both of the lines. Are the angles still equal in measure? _______ 6) Look at the diagram of intersecting lines below.