.jpg)
TOPIC 1:
TRANSFORMATION AND SYMMETRY
Lesson 1:
Transformation
This lesson introduces the concept of
transformations that alter the position or size of geometric shapes without
changing their fundamental properties. Key transformations include:
- Translation:
Moving a shape without rotating or resizing it.
- Rotation: Turning a shape around a fixed point.
- Reflection:
Flipping a shape over a line to create a mirror image.
- Dilation: Resizing a shape proportionally from a
fixed point.
- Example: Rotating a triangle 90 degrees around
its centroid will change its orientation but keep its shape and size the
same.
Lesson 2:
Line Symmetry
This lesson covers line symmetry, where a
shape can be divided into two identical halves that are mirror images of each
other.
- Example: A butterfly's wings exhibit line
symmetry along the body line, creating mirror images on either side.
Lesson 3:
Rotational Symmetry
Explains rotational symmetry, where a shape
can be rotated around a central point and still look the same at specific
angles of rotation.
- Example: A regular pentagon has rotational
symmetry at 72-degree intervals (360°/5).
Lesson 4:
Scale Drawing
Focuses on scale drawings, which are used to
represent objects proportionally smaller or larger than their actual size using
a specific scale factor.
- Example: On a map, 1 inch representing 10 miles
helps in visualizing large areas in a manageable format.
TOPIC 2:
SIMILARITY AND CONGRUENCE
Lesson 5:
Similar Figures
Explores figures that have the same shape but
may differ in size. They have equal corresponding angles and proportional
corresponding sides.
- Example: Two rectangles with side lengths in the
ratio 2:3 is similar if their corresponding angles are equal.
Lesson 6:
Similar Triangles
Discusses the criteria for triangle
similarity, including:
- AA (Angle-Angle): Two
angles in one triangle are equal to two angles in another triangle.
- SSS (Side-Side-Side):
Corresponding sides are proportional.
- SAS (Side-Angle-Side): Two
sides and the included angle are proportional and equal respectively.
- Example: Triangles with angles of 30°, 60°, and
90° are similar to each other if their sides are in proportion.
Lesson 7:
Area of Similar Triangles
Examines the relationship between the areas of
similar triangles, where the ratio of their areas is the square of the ratio of
their corresponding sides.
- Example: If two similar triangles have side
lengths in the ratio 1:2, their areas will be in the ratio 1:4.
Lesson 8:
Congruent Figures
Describes figures that are identical in both shape
and size and can be superimposed perfectly onto each other.
- Example: Two squares with equal side lengths are
congruent.
Lesson 9:
Congruent Triangles
Explains conditions for triangle congruence:
- SSS (Side-Side-Side): All
three sides of one triangle are equal to all three sides of another
triangle.
- SAS (Side-Angle-Side): Two
sides and the included angle are equal.
- ASA (Angle-Side-Angle): Two
angles and the included side are equal.
- Example: Two triangles with sides 5 cm, 5 cm,
and 7 cm that match in order are congruent.
TOPIC 3:
CIRCLES
Lesson 10:
The Circle and Its Parts
Introduces key components of a circle:
- Centre: The point equidistant from all points
on the circumference.
- Radius: The distance from the centre to any
point on the circumference.
- Diameter: Twice the radius; the distance across
the circle through the centre.
- Chord: A line segment with both endpoints on
the circumference.
- Arc: A part of the circumference.
- Sector: The area enclosed by two radii and an
arc.
- Example: The radius of a circle is 5 units, so
the diameter is 10 units.
Lesson 11:
Circumference of a Circle
Teaches how to calculate the circumference of
a circle using the formula C=2πrC = 2\pi rC=2πr, where rrr is the radius.
- Example: For a circle with a radius of 7 units,
the circumference is 14π14\pi14π units.
Lesson 12:
Area of a Circle
Explains how to calculate the area of a circle
using the formula A=πr2A = \pi r^2A=πr2.
- Example: For a circle with a radius of 5 units,
the area is 25π25\pi25π square units.
Lesson 13:
Segment of the Circle
Covers the area of a circle segment, which is
the region bounded by a chord and the arc it subtends. The area of a segment is
found by subtracting the area of the triangle formed by the chord and the
center from the area of the sector.
- Example: To find the area of a segment,
calculate the area of the sector and subtract the area of the central
triangle.
TOPIC 4:
CONSTRUCTION
Lesson 14:
Drawing Solid Figures
Focuses on techniques for drawing three-dimensional
figures, such as:
- Cubes: Drawing with visible edges and correct
perspective.
- Cylinders: Illustrating depth and curvature.
- Pyramids: Showing the base and triangular faces
with proper shading.
- Example: Drawing a cube with perspective to show
its three-dimensional structure.
Lesson 15:
Construction of a Triangle
Explains the construction of a triangle given
specific conditions like SSS, SAS, or ASA:
- Example: Constructing a triangle with side
lengths of 3 cm, 4 cm, and 5 cm using a ruler and compass.
Lesson 16:
Line Bisector
Teaches the construction of a perpendicular
bisector, which divides a line segment into two equal parts at a right angle.
- Example: Using a compass to find the midpoint of
a line segment and drawing a perpendicular line through it.
Lesson 17:
Angle Bisector
Explains how to construct an angle bisector,
which divides an angle into two equal parts.
- Example: Bisecting a 60° angle to create two 30°
angles using a compass and straightedge.
Lesson 18:
Construction of Regular Shapes
Covers the construction of regular polygons,
like pentagons and hexagons, using tools such as a compass and straightedge.
- Example: Constructing a regular hexagon
inscribed in a circle.
Lesson 19:
Nets
Describes nets, which are two-dimensional
shapes that can be folded to form three-dimensional solids. Each face of the
solid is part of the net.
- Example: The net of a cube consists of six
connected squares, which can be folded to form the cube.
Comments