Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Identify and classify different types of angles.
• Classify triangles by their sides and angles.
• Identify and classify different types of quadrilaterals.
• Calculate unknown angles in triangles and quadrilaterals.

Lesson summary

Geometry is all around us! From the shape of a soccer ball to the design of our homes, understanding shapes like triangles and quadrilaterals (four-sided shapes) helps us make sense of the world. In South Africa, geometry plays a crucial role in building and construction, architecture, and even the patterns in traditional art and craftwork. Knowing about angles and shapes will equip you with skills that are valuable in many aspects of your life, from designing your dream house to understanding how bridges are built to appreciating the beauty of Ndebele patterns.

Lesson notes

Let's dive into the world of angles, triangles, and quadrilaterals! 2.1 Angles: An angle is formed when two lines meet at a point (called the vertex). We measure angles in degrees (°).

Acute Angle: An angle less than 90°. Think of a small tilt.

Right Angle: An angle exactly 90°. Looks like the corner of a square.

Obtuse Angle: An angle greater than 90° but less than 180°. It's a wider tilt than a right angle.

Straight Angle: An angle exactly 180°. It forms a straight line.

Reflex Angle: An angle greater than 180° but less than 360°. It's like going around the clock more than halfway.

Revolution (Full Angle): An angle exactly 360°. A full circle.

Example 1: Imagine the hands of a clock. At 3 o'clock, the angle between the hour and minute hand is a right angle (90°). At 1 o'clock, the angle is acute. At 5 o'clock, the angle is obtuse. At 6 o'clock, the angle is a straight angle (180°).

Example 2: Using a Protractor Let's say we want to measure an angle. Place the center point of the protractor on the vertex (where the two lines meet). Align one line with the 0° mark on the protractor. Then, see where the other line crosses the protractor's scale. That number is the angle in degrees. It is important to check whether you are reading the inner or outer scale depending on which way the angle opens. 2.2 Triangles: A triangle is a closed shape with three sides and three angles. The sum of the angles inside any triangle is always 180°.

Classifying Triangles by Sides: Equilateral Triangle: All three sides are equal in length, and all three angles are equal (60° each).

Isosceles Triangle: Two sides are equal in length, and the two angles opposite those sides are also equal.

Scalene Triangle: All three sides are of different lengths, and all three angles are different.

Classifying Triangles by Angles: Acute-angled Triangle: All three angles are acute (less than 90°).

Right-angled Triangle: One angle is a right angle (90°). The side opposite the right angle is called the hypotenuse.

Obtuse-angled Triangle: One angle is obtuse (greater than 90°).

Example 3: Let's say a triangle has angles of 50°, 60°, and 70°. It's an acute-angled triangle because all angles are less than 90°. It's also a scalene triangle because no angles are the same, so no sides are the same length.

Example 4: A triangle has angles of 90°, 45°, and 45°. It's a right-angled triangle. It's also an isosceles triangle because two angles are equal, so two sides are equal. 2.3 Quadrilaterals: A quadrilateral is a closed shape with four sides and four angles. The sum of the angles inside any quadrilateral is always 360°.

Square: All four sides are equal, and all four angles are right angles (90°).

Rectangle: Opposite sides are equal and parallel, and all four angles are right angles (90°).

Parallelogram: Opposite sides are equal and parallel. Opposite angles are equal.

Rhombus: All four sides are equal. Opposite angles are equal.

Note: a square is a special kind of rhombus.

Trapezium: (Also sometimes called a trapezoid) Has at least one pair of parallel sides.

Kite: Two pairs of adjacent sides are equal.

Example 5: Consider a parallelogram. If one angle is 110°, the opposite angle is also 110°. Since the sum of all angles is 360°, the other two angles must each be (360° - 110° - 110°) / 2 = 70°.

Example 6: Angles in a Trapezium If a trapezium has two parallel sides and one angle is 60 degrees and another is 120 degrees and these two angles are adjacent to the same parallel side, then you have supplementary angles on that side. The other two angles would also be supplementary. Guided Practice (With Solutions)

Question 1: Classify the angle shown below, which measures 135°.

Solution: The angle is greater than 90° but less than 180°.

Therefore, it is an obtuse angle.

Question 2: A triangle has angles measuring 30° and 80°. What is the measure of the third angle? What type of triangle is it (classify by angles)?

Solution: The sum of angles in a triangle is 180°. Third angle = 180° - 30° - 80° = 70° All angles are less than 90°, so it's an acute-angled triangle.

Question 3: One angle in a parallelogram measures 65°. What are the measures of the other three angles?

Solution: Opposite angles in a parallelogram are equal. So, one other angle is also 65°. The sum of all angles in a quadrilateral is 360°. The remaining two angles are equal to each other, so each measures (360° - 65° - 65°) / 2 = 115°. The angles are 65°, 65°, 115°, and 115°.

Question 4: A quadrilateral has angles of 80°, 100°, and 80°. What is the fourth angle?

Solution: The sum of angles in a quadrilateral is 360° Fourth Angle = 360 - 80 - 100 - 80 = 100° Independent Practice (Questions Only) Draw and label an example of each type of angle: acute, right, obtuse, straight, reflex. A triangle has two sides of equal length. One angle measures 40°. What are the possible measures of the other two angles? (Hint: there are two possible answers) Can a triangle have two right angles? Explain why or why not.