STRAND 3.0 GEOMETRY.pptx cbc grade 6 for leaners

1. STRAND 3.0 GEOMETRY
LINES

2. LINES
• By the end of the sub- strand, the learner should be able to;
• Draw parallel lines in different situations,
• Bisect lines by construction,
• Construct perpendicular lines indifferent situations,
• Appreciate use of lines in daily life

3. Constructing parallel lines
a Parallel lines
Two or more lines are parallel if:
(a) they never meet.
(b) the distance between anų two such lines is the same.
Group Activity
In pairs:
1Draw a pair of lines using the two edges of a ruler. Label the lines AB and CD.
2. Place the edge of the ruler on line AB.
3. Place right corner at point and the shorter edge on AB.
4. Mark point Q on the other shorter edge of the right corner to lie on CD.
5.Slide the right corner along AB. What do you notice about the point Q on the right corner
and line CD?

4. Note
1 Line AB is parallel to line CD, that is, AB//CD.
2 For any pair of parallel lines, the distance between them is the same.

5. Assessment
• In pairs, use a ruler to draw four sets of parallel lines facingdifferent
directions.
• 2. Usea right corner and a ruler to identifų which of the pairsof lines
shown are parallel.

6. Constructing paralel lines using a pair of
compasses and a ruler
• Group Activity
• Draw a line parallel to PQ through point R.
• In pairs
• Copy the diagram showing line PQ and point R.
• 2. Using Q as the centre and radius PR, draw an arc above line PQ.
• 3. With R as the centre and radius PQ, draw an arc to cut the first arc
at T.
• 4. Join R to T to R
• 5. Discuss the results and share with other groups.

7. .R
P Q
Note
i) PQ is parallel to RT, that is, PR//RT.
i) The distance between line PQ and RT is the same.
ii) Line PQ and RT can never meet.

8. Example
• Use a pair of compasses and a ruler to draw aline parallel to CD
through point F.
.F
C
D

9. SOLUTION
F
C E
D
Use centre D, radius CF to make an arc above CD. Show arcs at E
(ii) Use centre F, radius CD to make an arc above CD to meet the first arc at E.
(iii) Join F to E. Therefore, CD//FE

10. ASSESSMENT
• Copy each of the following diagrams. For each diagram, use apair of
compasses and a ruler to construct a line parallel to thegiven line
through the marked point.
T .B
D .K
K .G O .A R .A
T P
L J G

11. Bisecting a line segment
Group Activity B
In pairs:
1. Draw a line segment AB.. A
2. With a radius greater than half of AB and centre A, make Arch above and
below AB
3 With the same radius and B as the centre, make arcs above and below AB
to intersect the first two arcs at C and D.
4. Join C to D to cut AB at P.
5. Measure AP and BP. What do you notice?
6. Discuss the results and share with other groups.

12. Note
1. AP=BP
2. P is the centre of line AB
3. To bisect a line is to divide a line into two equal parts

13. Example
Bisect line PR shown below. Mark point T the centre of line PR.
Measure line: (a) PR (b) PT (c) TR
solution P R
PR=7.2cm
PT =3.6cm
P T R TR=3.6cm

14. Assessment
Bisect the following lines
k
u
l
d m
o n
y

15. Drawing a perpendicular line using a set
square and a ruler
Perpendicular line through a point outside a given line
Group Activity
Draw a line perpendicular to AB through point D.
.D
A B

16. GROUP ACTIVITY
In groups of three:
1.Copy the diagram shown.
2.Place the edge of the ruler on line AB.
3.Place the set square, with the shorter edge on the ruler.
4.Slide the set square until the other shorter edge of the setsquare lies on point
D.
5. Draw a line through D to cut AB at C.
6. Measure angle ACD and angle BCD
7 Discuss the results and share with other groups.
NOTE
Line DC is perpendicular AB at C

17. Example
• use a set square and a ruler to draw a line perpendicular to AB to AB
through C
.C
A
B

18. SOLUTION
.C
A D B

19. Perpendicular line through na point on a
given line
(i) Group Activity
In the diagram below. draw a line perpendicular to line AB through point C.
In pairs
Copy the diagram shown.
2. Place the right corner of the set square at point C and one of the shorter
edges on line AB.
3. Draw a line through C and mark point D.
4.Measure angle ACD and angle DCB . What do you notice?
5. Discuss you results and share with other groups.

20. Note
Line DC is perpendicular to line AB.
Example
Draw a perpendicular line through point Eon CD using a set square and
a ruler.

21. ASSESSMENT
• Copy each of the diagrams shown below. Use a set square and a ruler to
draw a line perpendicular to each of the given lines through the point
shown .h
k
.y
j
a .c o
e
b

22. 3.2 ANGLES
• By the end of the sub strand, the learner should be able to;
• Identify angles on a straight line at a point in different situations,
• Measure angles on a straight line at a point in different situations,
• Work out sum of angles on a straight line in different situations,
• Determine the sum of angles in rectangles and triangles
• Construct equilateral, right angled and isosceles triangles,
• Measure the interior angles of equilateral, right angled and isosceles
triangles,
• Appreciate use of angles in real life

23. Angles on a straight line
Identifying angles on a straight line
Group Activity
Draw a straight line AC.
2. Mark a point B on the line.
3. Mark points D and E above line AC.
4.Join B to D and B to E.
5. Read the three angles made.
6. What do you notice?
7. Discuss your results and share with other groups.

24. Note
• Angles formed are ABD, DBE, EBC.
• (i) The three angles are on a straight line.

25. Note
i)mangle formed are AMD ,DBE, EBC
ii)The three angle are on a straight line
Example
The figure below is a straight line PR with point Q on line
Make three angles on line PR using the points S and T. Write the angles.
.s
.t
p q r

26. Solution
s
t
p r
q

27. ASSESSMENT
• Copy each of the diagrams shown below. Use a set square and a ruler to
draw a line perpendicular to each of the given lines through the point
shown .h
k
.y
j
a .c o
e
b

28. Measuring angles on a straight line in degrees
Group Activity
In groups of three
1.Draw a straight line PR.
2. Mark point Q on the line. Mark also points S and T on the same side
of PR.
3. Make three angles on line PQR using points S and T.
4. Use a protractor to measure the three angles.
5. Add the three angles
6. Discuss the results and share with other groups.

29. Note
(i) Angles PQS, SQT and TQR form angles on a straight line.
(ii) The sum of angles on a straight line is 180°.
(iii) Angles can be named using letters as shown.
D
a+b=1800
B a b c

30. Assessment
In each of the following:
(i) Measure the marked angles.
(ii) (ii) Find the sum of the angles on the straight line
a b c d
(i) e f m k

31. Angles in a triangle
• Sum of angles in a triangle
Group Activity 4
In groups of three: A
I. Draw any triangle ABC on a manila paper.
2. Label the angles A, B, C as a, band c.
3. Cut out the triangle ABC.
4. Cut off the angles marked a, b and c. B C
5. Arrange the angles marked on a straight line as shown.
6.What do you notice?
7. Discuss the results and share with other groups.

32. NOTE
i. The angles marked a, b and c form a straight line.
ii. (ii) a + b + c= 180°
iii. (ii) 180° = 2 x 90° (90° is a right angle)
=2 right angles
(iv) The sum of angles in a triangle is equal to 2 right angles.

33. ASSESSMENT
In groups of five:
(i) Trace and draw on a manila paper each of the triangles shown.
(ii) (ii) Cut out the triangles.
(iii) (iii) Cut off the angles and arrange them to form angles on a line.

34. angles of a triangle
Group Activity
In groups of three: A
I. Draw any triangle ABC.
2. Label the angles at A, B and C as a, b and C.
3. Use a protractor to measure angles marked a, b and c. B C
4. Find the sum of a, b and c.
5. What do you notice?
6. Discuss the results and share with other groups.
Note
(i) a + b + c= 180°.
(ii) The sum of angles in a triangle is equal to two right angles.
(iii) In a triangle, a right angle or 90° is marked as shown.

35. ASSESSMENT
IN the figure below measure the angle marked x,y,z
What is the sum of x,y,z
G
x=7
Y=56
Z=46
x+y+z H J
=78+56+46=180

36. Assessment
• Measure the angles of each triangle and find the sum of the angles in
each case.

37. Using angle sum of a triangle
Group Activity
In pairs:
1. Draw any triangle ABC.
2. Measure the angles at A and B.
3. Without measuring, find the size of the angle at C.
4. Discuss the results and share with other groups.

38. Example
• Find the size of the angle marked yin the figure shown
• 105
• Solution y 40
• y+105+40=180 angle sum of a triangle
• Y+145=180
• Y=180-145
• =35

39. ASSESSMENT
• Find the size of the angle marked with a letter in each of thefollowing:
• 7
a
70
40
e
60
g
50 70
35

40. 3.3 3-D OBJECT
• By the end of the sub strand, the learner shouldbe able to;
• Identify vertices, faces and edges in cuboids and cubes in different
situations,
• Identify faces and edges of cylinders in different situations,
• Describe plane figures in 3- d objects in the environment,
• Appreciate use of 3-D objects in real life

41. Identifying 3-D objects in the environment
Group Activity
In groups:
1.Take a chalk box, a tin and a packet of milk with triangularfaces.
2. Discuss the differences in their shapes.
3. Share your results with other groups.
. CHALK Mango juice milk
CHALK

42. Cuboids and cubes
Group Activity A
In groups of five:
1. Use a cuboid and trace three different faces A, B and C.
2. Try to fit each of the other faces on the traced faces A, B and C.
3. Share your findings with other groups.
Group Activity
In groups of five:
1.Use a cube and trace one face.
2. Try to fit each of the other faces on the traced face. What do you notice?
3. Count the number of sides and faces.
4. Compare the cube.
5. Share your observations with other

43. Note
• A face of a cuboid or cube is a flat surface formed by four lines
• (i) Two faces meet to form an edge
• (iii) Three edges or faces meet to form a corner or vertex.
• (iv) The plural of vertex is vertices.

44. assessment
• Fill in the correct number
• A cuboid has
a)………faces
b)………..edges
c)………vertices
2 write the correct number
A cube has
a)…… equal faces
b)…..edges
c)…….vertices

45. Cylinders
• Group Activity
• In groups of five
• 1. Use a can to identify parts of cylinder.
• 2. Trace one of the circular edges of the can.
• 3. Try to fit the other circular edge on the traced edge. What do you
notice?
• 4. Discuss and share your observations with other groups.
• Note
• i)A cylinder has two circular faces.
• (ii) The other face of the cylinder is round or curved.

46. 1. A cylinder has acicular…… edges.
2. What is the shape of the bottom or top face of a cylinder?
3. Identify three uses of cylinders.
4. Name the parts of a cylinder.

47. Pyramids
a Triangular based pyramid
Group Activity
In pairs and using a triangular based pyramid
1. Identify the parts of a triangular based Pyramid.
2. Count the number of edges, vertices and faces of the pyramid.
3. I densify the shape of the faces.
4. Discuss and share y your results with other groups.

48. Assessment
• 2. Using triangular based pyramid, complete the following:
• (a)……….faces meet to form a vertex..
• b)………..faces meet to form an edge.
• 3. Name the parts of a triangular based pyramid

49. Square based pyramid
• Group Activity
• In groups of five:
• (a) Discuss the parts of a square based Pyramid.
• (b) Trace one of the triangular faces.
• c) Fit each of the other triangular faces on the traced face. What do
you notice?
• (d) Discuss the parts of a square based Pyramid.
• (e) Share your observations with other groups.

50. Assessment
1. How many triangular faces are in a square based pyramid?
2. Name two uses of square based pyramids. Rectangular based
pyramids

51. Rectangular based pyramids
Group Activity
In groups of five:
1. Discuss the parts of a rectangular based Pyramid.
2. Use a model of the pyramid to trace two different faces A and B.
3.Try to fit the other two triangular faces on the traced faces What do you
notice?
4. Discuss the results and share with other groups.