Angles Lesson. Interwrite Interactive Mode software*. Sunshine State Standard: B.2.4.1, C.2.4.1

Transcription

1 Angles Lessn Sunshine State Standard: B.2.4.1, C Materials: Students: Paper (lined), pencil, straight edge, prtractr, patty paper (Optinal: A cmputer with the use f GeGebra, dynamic gemetry sftware.) Teacher: GTCO-CalCmp Interwrite Schlpad, patty paper, Angles GWB file. Objectives: 1. Students will learn hw t measure an angle. 2. Students will understand the prperties f a linear pair f angles. 3. Students will understand the relatinship between a vertical pair f angles. 4. Students will identify and find the relatinship f angles frmed by tw parallel lines cut by a transversal. Vcabulary: Linear pair f angles, cngruent, supplementary angles, cmplementary angles, cnjecture, vertical angles, parallel lines, transversal, crrespnding angles, alternate interir angles, alternate exterir angles, prtractr, right angle. Lessn Plan: -Hw t measure an angle. Have the students each draw an angle, it desn t matter if the angle is acute r btuse, ask the students nt t draw a right angle thugh. Handut the prtractrs and have students measure their angles. As students measure their angles the instructr shuld mdel the behavir by the use f Interwrite Interactive Mde sftware*. *Nte: See Angles_Lessn_interwrite Created by: Guy Barmha

2 A pssible questin a student may ask is: Which numbers d I use, inside r utside nes? This will be a gd pprtunity t discuss which numbers t use and why. Let students try t answer the questin f which set f measurements t use. Have students express their arguments as t which numbers t use. Hpefully yur students will cme up with the crrect slutin f using the inside numbers ging cunter-clckwise and the utside numbers ging clckwise. Cunter Clckwise Clckwise Pints t emphasize: The center f the prtractr needs t be at the vertex f the angle. Line up ne f the rays f the angle with the zer line n the prtractr. Created by: Guy Barmha

3 -Students will draw a pair f linear angles. Encurage students t draw a different lking picture than the ne the teacher draws, fr example here are tw different lking pair f angles. Each student will label the left angle 1 and the right angle 2. Students will use their prtractr t measure bth angles frmed. T get the students invlved with their neighbrs images have each student draw a set f linear angles and then pick tw different classmates, ne t measure Angle 1 and ne t measure Angle 2. Cmpile a list f students results. The list may lk like the ne belw: m , Yur list shuld be lnger than this s the students m , can have enugh data t make a cnjecture. m 1 140, 40 m 1 37, 145 m 1 100, 80 m 1 69, 110 After students have cmpiled a list big enugh, ask them t: Make a cnjecture abut the measures f the tw angles. The students shuld ntice that the angle pairs sum t 180. (Nte: Nt all angle pairs will sum t exactly 180, hwever, the sums shuld all be clse enugh t 180 fr the students t make a prper cnjecture) Nw will a great time t ask the students: Why dn t all the linear angle pairs add up t the same number? Allw students t discuss sme f the reasns they came up with. Reasns shuld include but nt be limited t: human errr, thickness f the lines, and imprper use f the prtractr. Created by: Guy Barmha

4 What d we call pairs f angles that add up t 180 degrees? Students shuld knw that a linear pair f angles are supplementary. This may be a gd time t review what it means fr tw angles t be supplementary as well as what it means fr tw angles t be cmplementary. G t wrksheet n linear pair f angles. Linear pair f angles wrksheet Created by: Guy Barmha

5 -Students will draw tw intersecting lines and label the angles frmed 1, 2, 3, 4 in either a clckwise r cunterclckwise rtatin. Students will nw be asked t: Make a cnjecture describing which angles are cngruent. Students shuld see that the vertical angles 1 and 3 are cngruent and the vertical angle 2 and 4 are cngruent. T prve this cnjecture the students will trace angle 1 with their patty paper and see if it fits n tp f angle 3. Then repeat the prcedure fr angles 2 and 4. Fr example, Students can see that the measure f angle 1 has t be the same as the measure f angle 3 G t wrksheet n vertical angles: Vertical Angles wrksheet Created by: Guy Barmha

6 -Students will use their straightedge and tw f the lines n their paper t draw tw parallel lines. Then they will draw a transversal t thse tw parallel lines and label the angles like the illustratin belw: (Remind the students t draw a different lking picture than the ne yu draw n the bard) Have students: Make a cnjecture abut the angles that are cngruent t each ther. Students shuld ntice that the crrespnding, alternate interir and alternate exterir angles are cngruent. Have students prve their cnjectures by again using their patty paper t trace angles 1, 2, 3, and 4 and placing their patty paper n tp f the ther fur angles t which nes match up. Tell the students that they can flip their patty paper 180 degrees t match up mre angles. This picture illustrates the students tracing angles 1, 2, 3, and 4. This picture illustrates that crrespnding angles are cngruent. Created by: Guy Barmha

7 This picture illustrates that alternate interir and alternate exterir angles are cngruent. (Only after the 180 degree rtatin f the patty paper.) After the students have bserved which angles are cngruent have them classify them. Fr example, Crrespnding Angles: 1 5, 2 6, 3 7, 4 8 Alternate Interir Angles: 3 6, 4 5 Alternate Exterir Angles: 1 8, 2 7. This wuld a great time t talk t the students abut the situatin when a transversal intersects tw nn-parallel lines. Ask the students what happens t the angle relatinships they just discvered. G t the parallel lines and transversal wrksheet: Parallel lines and transversal Created by: Guy Barmha