Day 26 Bellringer. 1. Given that the pair of lines intersected by the transversal are parallel, find the value of the x in the following figures.

Transcription

1 Day 26 Bellringer 1. Given that the pair of lines intersected by the transversal are parallel, find the value of the x in the following figures. (a) 2x x 41 (b) 9x x (c) x x HighSchoolMathTeachers@2018 Page 1

2 Day 26 Bellringer 2. In the figure below, MN and PQ intersect at O as shown. M P O 2r 111 r + 24 Q N (a) Find the value of r. (b) Hence, find MOP : HighSchoolMathTeachers@2018 Page 2

3 Day 26 Bellringer Answer Keys Day 26: 1. (a) x = 58 (b) x = 9 (c) x = (a) r = 135 (b) MOP = 21 HighSchoolMathTeachers@2018 Page 3

4 Day 26 Activity 1. Place the carbon paper between the two plain papers provided make sure they are carefully aligned. 2. Draw two intersecting lines (at any angle), PQ and RS on the top plain paper. 2. Label the intersection point O as shown below. P S O 3. Label the two pairs of vertical angles as shown below. R Q P α β O β α S R Q 4. Separate the two papers and on the duplicate, cut out carefully angles α and β using the pair of scissors provided. HighSchoolMathTeachers@2018 Page 4

5 Day 26 Activity 5. Place the cut out of angle α on angle α on the original plain paper. What do you notice? What does this suggest about the two angles? 6. Place the cut out of angle β ón angle β on the original plain paper. What do you notice? What does this suggest about the two angles? Page 5

6 Day 26 Activity In this activity, students will be able to verify that vertical angles are equal in preparation for the lesson. The students will work in groups of four. Each group will be provided with two A4 size plain papers, an A4 size carbon paper, a pencil, a ruler, a pair of scissors. Answer Keys Day 26: 1. No response 2. No response 3. No response 4. No response 5. The cut outfits exactly on the angle suggesting that the angles are equal. 6. The cut outfits exactly on the angle suggesting that the angles are equal. HighSchoolMathTeachers@2018 Page 6

7 Day 26 Practice Use the figure below to answer questions PQ and RS are parallel. AB intersects the two parallel lines at points K and L. We are given LKQ = β. 1. Find the measure of LKP in terms of β. 2. Find the measure of KLS in terms of β. 3. Compare KLS to LKP. What do you discover about the two angles? 4. Find the measure of KLR in terms of β. 5. Compare LKQ to KLR. What do you notice about the two angles? 6. Find the measure of AKQ in terms of β. 7. Find the measure of BLR in terms of β. 8. Compare AKQ to BLR. What do you conclude? 9. Find the measure of AKP in terms of β. 10. Find the measure of BLS in terms of β. 11. Compare AKP to BLS. What do you notice? HighSchoolMathTeachers@2018 Page 7

8 Day 26 Practice Use the figure below to answer questions Lines AB and CD intersect to form the angles shown and DOB = θ. D A O θ C 12. Find the measure of AOD in terms of θ. B 13. Find the measure of BOC in terms of θ. 14. Compare AOD to BOC. What do you notice about these two angles? 15. Find the measure of AOC in terms of θ using the measure of AOD. 16. Compare DOB to AOC. What do you notice about these two angles? Use the figure below to answer questions JK and LM are parallel. PQ intersects the two parallel lines at points to form the angles shown and KAP = p. 17. Find the measure of JAP in terms of p. HighSchoolMathTeachers@2018 Page 8

9 Day 26 Practice 18. Find the measure of BAK in terms of p. 19. Find the measure of BAJ in terms of p using the measure of BAK you have found in question 18 above. 20. Compare BAJ to KAP and write done your conclusion about the measures of the two angles. HighSchoolMathTeachers@2018 Page 9

10 Day 26 Practice Answer keys Day 26: 1. LKP = 180 β 2. KLS = 180 β 3. LKP = KLS = 180 β; They are equal 4. KLR = β 5. LKQ = KLR = β; They are equal 6. AKQ = 180 β 7. BLR = 180 β 8. AKQ = BLR = 180 β;they are congruent 9. AKP = β 10. BLS = β 11. AKP = BLS = β; They are equal θ θ 14. They are equal 15. θ 16. They are equal p p 19. p 20. They are congruent HighSchoolMathTeachers@2018 Page 10

11 Day 26 Exit Slip In the figure below, KL and MN are parallel. PQ intersects the two parallel lines at points A and B. We are further given BAL = θ. P K A θ L M B N Q (a) Find the measure of ABN in terms of θ. (b) Using the expression for the measure of ABN you have found in part (a) above, find the measure of ABM in terms of θ. (c) Compare ABM to BAL. What do you discover about the two angles? HighSchoolMathTeachers@2018 Page 11

12 Day 26 Exit Slip Answer Keys Day 26: (a) ABN = 180 θ (b) ABM = θ (c) ABM = BAL = θ; The two angles are congruent. HighSchoolMathTeachers@2018 Page 12

13 Day 27 Bellringer 1. A straight line AB passes through points K(8,4) and L(4,2). a) Find the slope of line AB. b) Find the equation of line AB. 2. A straight line KL passes through points M(5,10) and N(7,6). a) Find the slope of the line. b) Find the equation of the line KL. 3. A Straight line AB passes through a point P(2,1). If the same line is subjected to a translation of 3 units upwards, what will be the new coordinates of point P? HighSchoolMathTeachers@2018 Page 13

14 Day 27 Bellringer Answer Key Day 4 1 a) 1 2 b) y= x 2 2 a) 2 b) y = 2x (2,4) HighSchoolMathTeachers@2018 Page 14

15 Day 27 Activity 1. Position the set square and the ruler as shown below. 2. Holding the ruler and the set square in the same position, carefully draw a line along the edge AB of the set square. 3. Holding the ruler in the same initial position, carefully slide the set square along edge CD of the ruler to another position in the direction shown below. HighSchoolMathTeachers@2018 Page 15

16 Day 27 Activity 4. In the same way, holding the ruler and the set square in the same position, carefully draw a line along the edge EF of the set square. 5. Leaving the ruler unmoved, carefully remove the set square and observe the pair of lines you have drawn. What kind of lines are they? 6. Compare the steepness of one line with respect to the other. What is your conclusion about the steepness of this pair of lines? 7. If you another line in the same way along position GH as shown below, what will be its steepness in comparison with the pair of lines you have drawn previously? C G H D 8. What conclusion regarding the type of lines in relation to their steepness do you deduce from the type of lines you have drawn in this activity? HighSchoolMathTeachers@2018 Page 16

17 Day 27 Activity In this activity, students will work in groups of four to discover the slope criteria of parallel lines by drawing three parallel lines and comparing the steepness. The students in the respective groups will require a pencil, a protractor, a set square and an A4 size plain paper. It is perceived that the students have discussed the basic properties of parallel lines. Answer Keys Day 27: 1. No response 2. No response 3. No response 4. No response 5. Parallel lines 6. They have the same steepness. 7. It will have the same steepness. 8. If two or more lines are parallel, then they have the same steepness HighSchoolMathTeachers@2018 Page 17

18 Day 27 Practice Two parallel lines AB and CD share a perpendicular bisector. Line AB passes through points A(3,4) and B(5,3). Line CD passes through points C(-2,8) and D(0,7). The perpendicular bisector passes through points Q(3,3) and R(4,5) Use this information to answer questions Find the slope of line AB. 2. What is the slope of line CD? 3. Compare the slope of line AB and that of line CD. 4. What is the slope of their perpendicular bisector? 5. Multiply the slope of line AB with that of the perpendicular bisector. What is their product? 6. Find the product of the slope of line CD and the slope of the perpendicular bisector. Two lines, L 1 and L 2 are parallel to each other. L 1 passes through points A(6,3) and B(4,6) while L 2 passes through points C(4,7) and D(2,10). Use this information to answer questions Find the slope of L 1 8. Find the slope of L 1 9. Compare the slope of L 1 and that of L 2 Two lines L 3 and L 4 are perpendicular to each other. L 3 passes through points E(5,8) and F(3,9) while L 4 passes through points G(1,2) and the origin. Use this information to answer questions Find the slope of L Find the slope of L What is the product of the slope of L 4 and that of L 3? HighSchoolMathTeachers@2018 Page 18

19 Day 27 Practice Lines ST and MN are parallel to each other. Line ST passes through points S(2,3) and T(5,9). Line MN Passes through points M(3,4) and N(6,10). Use this information to answer questions 13 to Find the slope of line ST 14. Find the slope of line MN 15. Compare the slopes of the two lines. Line PT crosses two lines L 5 and L 6 such that it makes a right angle with them. Line PT passes through points P(4,7) and T(2,1), L 5 passes through points A(12,9) and B(9,10) and L 6 passes through points G(4,3) and F(1,4). Use this information to answer questions 16 to Find the slope of line PT 17. Find the slope of L Find the product of the slope of line PT and the slope of L Find the slope of L Find the product of the slope of line QR and the slope of L 6 HighSchoolMathTeachers@2018 Page 19

20 Day 27 Practice Answer Keys Day 27: They are equal They are equal They are equal HighSchoolMathTeachers@2018 Page 20

21 Day 27 Exit Slip 1. Two lines AB and CD are perpendicular to each other, and they intersect at a point V(3,6). Line CD passes through a point U(6,15) while line CD passes through a point W(0,7). a) What is the slope of line AB? b) Find the slope of line CD C) Find the product of slope of line AB and the slope of line CD. HighSchoolMathTeachers@2018 Page 21

22 Day 27 Exit Slip Answer Keys Day 27: 1. a) 3 b) 1 3 c) -1 HighSchoolMathTeachers@2018 Page 22

23 Day 28 Bellringer 1. Two lines AB and CD are such that and the former passes through points A(2,3) and B(4,7) while the latter passes through points C(1,2) and D(4,8). a) Find the slope of line AB b) Find the slope of line CD. 2. Two lines DF and DH intersect at point D(3,2). Line DF and DH pass through the point F(5,4) and H(4,3) respectively. a) Find the slope of line DF b)find the slope of line DH 3. Find the slope of a line that is perpendicular to another whose slope is 3. HighSchoolMathTeachers@2018 Page 23

24 Day 28 Bellringer Answer Key Day 4 1 a) 2 b) 2 2 a) 1 b) HighSchoolMathTeachers@2018 Page 24

25 Day 28 Activity 1. Plot the XY plane with a scale of two bigger squares representing one unit as shown below. 2. Mark points 1, 1 and 2,1 and label them A and B respectively. HighSchoolMathTeachers@2018 Page 25

26 Day 28 Activity 3. Join points A and B with a straight line as shown below. 4. Mark points 3, 1 and (-1,2) and label C and D respectively. 5. Using a ruler and a pencil join points C and D with a straight line as shown below. 6. Label the point of intersection of lines AB and CD as F. 7. Identify any two points on line AB and use them to find the slope of line AB. What do you get as the slope of line AB? 8. Identify any two points on line CD and use them to find the slope of line CD. What do you get as the slope of line CD? 9. Multiply the slope of line CD with the slope of line AB. What is their product? 10. Using a protractor measure AFC. What the size of AFC? HighSchoolMathTeachers@2018 Page 26

27 Day 28 Activity In this activity, students are required to draw two lines in XY-plane, find their slopes and measure the angle between them. Students are required to work in groups of at least three. Each group is required to have a ruler, a pencil, a graph paper and a protractor. Answer Keys Day 28: 1-6. No response HighSchoolMathTeachers@2018 Page 27

28 Day 28 Practice Use the following information to answer questions 1 and 2. Line AB is parallel to CD and passes through the points A(1,2) and B(4,4).If line CD passes through point D 3,7 ; 1. Find the slope of line AB 2. Find the equation of line CD Use the following information to answer questions 3-5. Two perpendicular lines ST and SV intersect at a point S(3,4). Line ST passes through point T(5,5). 3. Find the slope of line ST. 4. Find the slope of the line SV 5. Find the equation of the line SV Use this information to answer questions 6-7. A-Line defined by y = 3x + 4 is perpendicular to line DF. If the coordinates of D is (2,4) 6. Find the slope of the line DF 7. Find the equation of the line DF Use the rectangle to answer questions DEFG is a rectangle. Two vertices of the rectangle are D 4,3 and E 7,1 8. Find the slope of side DE 9. What is the slope of the side GF? 10. Find the slope of the side EF 11. Find the equation of side EF 12. What is the slope of side DG? HighSchoolMathTeachers@2018 Page 28

29 Day 28 Practice 13. If a line is drawn such that it coincides with the side DG, what will be the equation of that line? Use this information to answer questions Lines TU and UV intersect perpendicularly at a point U 31,9. If the coordinates of T is 11, Find the slope of the line TU 15. What is the slope of the line UV? 16. Find the equation of the line UV Use the following information to answer question Line PR is parallel to line ST and passes through points P 5,0 and R 2,9. Line ST passes through a point S 2, Find the slope of the line PR 18. What is the slope of the line ST? 19. Find the equation of the line ST. 20. Two perpendicular lines L 1 and L 2 intersect at a point A 11, 4. L 1 passes through a point B 3,5. Find the equation of L 2 HighSchoolMathTeachers@2018 Page 29

30 Day 28 Practice Answer Keys Day 28: y = 2 3 x y = 2x y = 1 3 x y = 3 19 x y = 3 2 x y = x y = 3x y = 14 9 x HighSchoolMathTeachers@2018 Page 30

31 Day 28 Exit Slip 1. ABCD is a square. Two of its vertices are A(2,4) and B(4,1) as shown below. D A(2,4) C B(4,1) Without drawing, find the equation of side BC HighSchoolMathTeachers@2018 Page 31

32 Day 28 Exit Slip Answer Keys Day 28: 1. y = 3 2 x 5 HighSchoolMathTeachers@2018 Page 32

33 Day 29 Bellringer 1. Find the distance between the following points (a). 2,4 and 6,4. b). 5,3, 5, 2 c). 3,8, 1, 2 2. The ratio of y to p is 3 5. If p = 35, find the value of y. 3. Jastine and Justo are to share 18 pieces of candy in the ratio 1: 2 respectively. How many more pieces of candies do Justo get more than Jastine? HighSchoolMathTeachers@2018 Page 33

34 Day 29 Bellringer Answer Key Day a). 8 units b). 5 units c) units HighSchoolMathTeachers@2018 Page 34

35 Day 29 Activity 1. Take out the rod, place it on the part and marks its ends on the paper. Label the marks as M1 and M2 respectively. 2. Place one end of the rod at M2 and the other end as a new mark, M3 where M3, M2and M1 must be on the same straight line. 3.Continue in that manner until you get M6 with M1 to M6 all lying on the same straight line. 4. How marks do you have in total? 5. How many spaces between the marks are there? 6. Identify mark 3, how many marks spaces (of the size of the rod) are before Mark Identify mark 3, how many marks spaces (of the size of the rod) are after Mark Find the ratio between the value in 6 and that of 7 respectively. 9. Let M1, M2,, M6 be on a line that is on x- axis where M1 is at the origin. What would be the coordinates of M1? 10. Identify the coordinates of M1, M3, and M6. HighSchoolMathTeachers@2018 Page 35

36 Day 29 Activity 11. Taking P = M3, verify that the formula x = mx 2+nx 1 ; y = my 2+ny 1 is true if P x, y is m+n m+n the coordinates of M3. HighSchoolMathTeachers@2018 Page 36

37 Day 29 Activity In this activity, we would like to verify the formula for proportional division of a line. Students will work in groups of 4. Each group will require a plain paper, a standard measurement tool which is a small grass rod (or small perspex rod or any other rod that can serve the purpose) of 2 into 3 in, pencil. Answer Keys Day 29: 1 3.No response ,0 10. M1 0,0, M3 2,0, M6 5,0 11.P 2,0 ; x = 2, y = 0, m: n = 2: 3, x 1 = y 1 = y 2 = 0; x 2 = 5 x = mx 2+nx 1 m+n = = 2 y = my 2+ny 1 m+n = = 0 HighSchoolMathTeachers@2018 Page 37

38 Day 29 Practice Use the following information to answer questions 1-3. Given the following endpoints of a line segment, A 3, 2 and B 6, 5, find the coordinates of the point that devides the line in the following ratios Use the following information to answer questions 4-9. Given the following endpoints of a line segment, C 8, 7 and D 8,1, find the coordinates of the point that devides the line in the following ratios. 4. 1: HighSchoolMathTeachers@2018 Page 38

39 Day 29 Practice Use the following information to answer questions The following endpoints of a line segment are M 2,4 and N. Point T 4, 2 divides the line in the ratio 1: Find the coordinates of N. 11. Find the coordinates of a point that divides the line in the ratio Find the coordinates of a point that divides the line in the ratio Find the coordinates of a point that divides the line in the ratio Find the coordinates of a point that divides the line in the ratio Find the coordinates of a point that divides the line in the ratio Find the coordinates of a point that divides the line in the ratio Find the coordinates of a point that divides the line in the ratio Find the coordinates of a point that divides the line in the ratio Use the following information to answer questions The following endpoints of a line segment are P 7, 5 and Q. Point S 3,1 divides the line in the ratio 2: Find the coordinates of a point Q. 20. If Q divides line PR in the ratio 3 1, find the coordinates of a point R. HighSchoolMathTeachers@2018 Page 39

40 Day 29 Practice Answer Keys Day 29: 1. 0, , , , , , , , , , , , , , , , , , , ,7 HighSchoolMathTeachers@2018 Page 40

41 Day 29 Exit Slip Find the coordinate of a point C dividing the line segment joining 1, 3 and 2,4 in the ratio 1.2. HighSchoolMathTeachers@2018 Page 41

42 Day 29 Exit Slip Answer Keys Day 27: 0, 1 HighSchoolMathTeachers@2018 Page 42