We explore properties of shapes, angles, and geometric reasoning. Students learn to use rules such as the angle sum of triangles, vertically opposite angles, and angles on a straight line.
The sum of angles in a triangle is 180°. When two lines intersect, vertically opposite angles are equal. Angles on a straight line add up to 180°, and angles around a point total 360°.
In a triangle, two angles measure 35° and 85°. Find the third angle.
180 − (35 + 85) = 60°
When two straight lines cross, one of the angles measures 120°. What is the size of the vertically opposite angle?
Vertically opposite angles are equal → 120°
We calculate perimeter and area of common shapes like rectangles, triangles, and circles. These skills help us solve problems involving fencing, flooring, and design.
Rectangle: A = l × w
Triangle: A = ½ × base × height
Circle: A = πr², Circumference = 2πr
A rectangular garden is 8 m long and 5 m wide. Find its area and perimeter.
A = 8 × 5 = 40 m², P = 2(8 + 5) = 26 m
A circle has a radius of 7 cm. Find its circumference (use π = 3.14).
C = 2 × 3.14 × 7 = 43.96 cm
We study 3D objects such as prisms, pyramids, and cylinders, finding their volume and surface area for practical applications like packaging and storage.
Cuboid: V = l × w × h
Cylinder: V = πr²h
Prism: V = area of cross-section × length
Find the volume of a rectangular box measuring 10 cm by 6 cm by 4 cm.
V = 10 × 6 × 4 = 240 cm³
A cylindrical container has a radius of 3 cm and a height of 12 cm. Calculate its volume (use π = 3.14).
V = 3.14 × 3² × 12 = 339.12 cm³
We explore transformations such as reflections, rotations, translations, and enlargements. Symmetry helps describe balance and pattern in geometric figures.
Transformations change a shape’s position, size, or orientation without altering its basic properties. Lines of symmetry and rotational symmetry describe how figures can be mapped onto themselves.
A triangle is reflected across the y-axis. If one vertex is at (4, 3), what are the coordinates of its image?
Reflection in y-axis → (-4, 3)
A square is rotated 90° clockwise about the origin. If one vertex is at (2, 1), find its new coordinates.
(x, y) → (y, -x) → (1, -2)