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.
• Calculate unknown angles in quadrilaterals.

Lesson summary

Geometry is all around us! From the shape of your classroom to the patterns on your clothing, understanding shapes, angles and their properties helps us make sense of the world. In South Africa, geometry is used in everything from building houses and designing roads to creating traditional patterns in art and craftwork. A solid foundation in geometry will help you excel in many subjects later on, and even inspire you to become an architect, engineer, or designer. This week, we'll focus specifically on angles, triangles, and quadrilaterals, building a strong base for future geometric explorations.

Lesson notes

Angles: An angle is formed when two lines or line segments meet at a point called the vertex. We measure angles in degrees (°).

Acute Angle: An angle less than 90°.

Example: 30°, 60°, 85°.

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

Obtuse Angle: An angle greater than 90° but less than 180°.

Example: 100°, 120°, 170°.

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

Reflex Angle: An angle greater than 180° but less than 360°.

Example: 200°, 270°, 300°.

Revolution (Full Rotation): An angle exactly 360°.

Using a Protractor: A protractor is a tool used to measure angles. Place the center of the protractor on the vertex of the angle, and align the base line of the protractor with one arm of the angle. Read the degree measurement where the other arm of the angle intersects the protractor's scale.

Triangles: A triangle is a closed shape with three sides and three angles. The sum of the angles in any triangle is always 180°.

Classification 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 equal.

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

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

Right-angled Triangle: One angle is a right angle (90°).

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

Example 1: Finding an Unknown Angle in a Triangle If a triangle has angles of 70° and 50°, what is the size of the third angle?

Solution: We know that the angles in a triangle add up to 180°. So, 70° + 50° + unknown angle = 180° 120° + unknown angle = 180° Unknown angle = 180° - 120° Unknown angle = 60° Example 2: Identifying Triangles A triangle has sides of lengths 5cm, 5cm, and 7cm. It also has angles of 60°, 60° and 60°. What type of triangle is it?

Solution: The triangle has two sides of equal length, so it's an isosceles triangle.

However, ALL its angles are equal, thus it is actually an Equilateral Triangle. It is an acute-angled triangle because all angles are less than 90°.

Quadrilaterals: A quadrilateral is a closed shape with four sides and four angles. The sum of the angles in 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 all four angles are right angles (90°).

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

Rhombus: All four sides are equal, and opposite angles are equal.

Trapezium (or Trapezoid): Only one pair of opposite sides are parallel.

Kite: Two pairs of adjacent sides are equal.

Example 3: Finding an Unknown Angle in a Parallelogram In a parallelogram, one angle measures 110°. What is the measure of the angle opposite to it, and the two adjacent angles?

Solution: Opposite angles in a parallelogram are equal.

Therefore, the opposite angle is also 110°. The sum of all angles in a quadrilateral is 360°. Let the unknown adjacent angle be 'x'. The opposite adjacent angle will also be 'x'. 110° + 110° + x + x = 360° 220° + 2x = 360° 2x = 360° - 220° 2x = 140° x = 140° / 2 x = 70° Therefore, the opposite angle is 110° and the adjacent angles are both 70°. Guided Practice (With Solutions)

Question 1: Measure the angle below using a protractor. Is it acute, obtuse, or right? [Image of an angle measuring approximately 60 degrees would be included here] Solution: Using a protractor, the angle measures approximately 60°. Since 60° is less than 90°, it is an acute angle.

Question 2: A triangle has two angles measuring 45° and 95°. What is the measure of the third angle? Is the triangle acute, obtuse, or right angled?

Solution: The angles in a triangle add up to 180°. 45° + 95° + unknown angle = 180° 140° + unknown angle = 180° Unknown angle = 180° - 140° Unknown angle = 40° The third angle is 40°. The triangle has angles of 45°, 95° and 40°. Because it has one angle greater than 90° (95°), it's an obtuse-angled triangle.

Question 3: Identify the following quadrilateral. Describe at least three of its properties. [Image of a Rhombus would be included here] Solution: The quadrilateral is a rhombus.

Properties: All four sides are equal in length. Opposite angles are equal. Opposite sides are parallel.

Question 4: One angle of a rectangle is 90°. What are the measurements of the other three angles?

Solution: All angles in a rectangle are right angles.

Therefore, all angles measure 90°. The other three angles are each 90°. Independent Practice (Questions Only) Draw an acute angle, an obtuse angle, and a right angle. Label each one clearly. A triangle has angles of 35° and 85°. What is the size of the third angle? What type of triangle is it? A triangle has side lengths of 8cm, 8cm, and 5cm. What type of triangle is it? What is the difference between a square and a rhombus?