π
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y = mx+b
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About this video
The Afrikaans recording of Grade 8 Mathematics Paper 2, November 2023 (Eastern Cape): geometry of straight lines, triangles and congruency, the Theorem of Pythagoras and quadrilaterals. The extra examples below are written in English.
What it covers
- Angle pairs: vertically opposite, corresponding, alternate, co-interior
- Triangles: the angle sum, isosceles and exterior angles
- Congruent triangles and their conditions
- The Theorem of Pythagoras
- Quadrilaterals: kite and rhombus; angles adding up to 360°
Extra worked examples
✍️ Extra example: co-interior angles between parallel lines are 3x + 15° and 2x + 15°. Find x and both angles.
- 1(3x + 15°) + (2x + 15°) = 180°Co-int ∠s add up to 180° (a U-shape).
- 25x = 150° → x = 30°Collect the like terms, then divide.
- 3The angles are 105° and 75°Substitute in brackets: 3(30°) + 15° and 2(30°) + 15°. Check: 105° + 75° = 180° ✓
✍️ Extra example: a 5 m ladder leans against a wall with its foot 1,4 m from the wall. How high up the wall does it reach?
- 1h² + 1,4² = 5²The ladder is the hypotenuse — it is opposite the right angle at the wall.
- 2h² = 25 − 1,96 = 23,04Subtract to find a shorter side.
- 3h = √23,04 = 4,8 mThe square root.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Corresponding angles on parallel lines are 2y + 10° and 70°. Find y.
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2y + 10° = 70° (corr ∠s) → y = 30° - 2An isosceles triangle has base angles of 64°. Find the third angle.
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180° − 64° − 64° = 52° (∠s of a △) - 3Is a triangle with sides of 7 cm, 24 cm and 25 cm right-angled? Show why.
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7² + 24² = 49 + 576 = 625 = 25², so yes - 4A kite has two unequal angles of 124° and 60°; its other two angles are equal. Find them.
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(360° − 124° − 60°) ÷ 2 = 88° each (∠s of a quad) - 5Name the quadrilateral with four equal sides whose opposite angles are equal but not 90°.
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A rhombus
Practise this topic
Download matching Grade 8 papers and worksheets.
