Grade 10 Maths · Paper 2

Euclidean Geometry Grade 10

Real past paper questions and answers from 2021 to 2024, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 55 past paper questions
skills: 16 skills
videos: 16 videos

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Question 5.1 · June 2024 · Paper 2 · Provincial · 2 marks

ABCD is a rhombus with the diagonals

A C = 16

cm and

D B = 30

cm.

5.1 Complete the theorem: The line segment joining the midpoints of two sides of a triangle is ...(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

What's in Euclidean Geometry Grade 10

Each skill is one thing a memo gives a tick for. Tap a skill for its own questions, notes and videos.

Lines, Angles and Triangles55 past paper questions

More Euclidean Geometry Grade 10 questions and answers

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1. Question 8.1.1 · November 2024 · Paper 2 · Provincial · 4 marks
ABCD is a parallelogram and AC is a diagonal, with A, F, E and C as collinear points. BE is parallel to FD.
8.1 Prove that:
8.1.1 $Δ A BE \equiv Δ C D F$ (4)
Show the memo (4 ticks)Memo
1. ✓
  S/R: AB = CD $A B = C D$ (opposite sides of parm)
  1 mark · Use properties of quadrilaterals
2. ✓
  S/R: Â₁ = Ĉ₂ $\hat{A}_{1} = \hat{C}_{2}$ (alt $∠$ s; $A B ∥ C D$ )
  1 mark · Use angles on parallel lines
3. ✓
  S/R: Ê₁ = F̂₁ $\hat{E}_{1} = \hat{F}_{1}$ (alt $∠$ s; $BE ∥ F D$ )
  1 mark · Use angles on parallel lines
4. ✓
  Conclusion $∴ Δ A BE \equiv Δ C D F$ (AAS)
  1 mark · Prove triangles congruent
2. Question 1.9 · March 2022 · Provincial · 2 marks
Four options are provided as possible answers to the following questions. Choose the correct option.
1.9 Which quadrilateral is equiangular but not always equilateral?(2)
1. A rectangle
2. B parallelogram
3. C rhombus
4. D square
Show the memo (1 tick)Memo
1. ✓
  Check propertiesRectangle has 90 degree angles (equiangular) but sides are not always equal.
  Answer: A
  2 marks · Prove or name a quadrilateral type
3. Question 4.1 · March 2022 · Provincial · 4 marks
4.1 In the diagram below, $Δ A BC$ is drawn with $A B ∥ ST$ , $\hat{C}_{1} = 10 x$ , $\hat{C}_{2} = y$ , $\hat{S}_{1} = 7 8^{\circ}$ , $\hat{T}_{1} = 4 x$ and $\hat{A} = z$ . Calculate, with reasons, $x, y$ and $z$ .(4)
Show the memo (3 ticks)Memo
1. ✓
  Calculate x $10 x = 7 8^{\circ} + 4 x$ (Ext $∠$ of $Δ$ CST)
  $6 x = 7 8^{\circ} ⟹ x = 1 3^{\circ}$
  2 marks · Use exterior angle of a triangle
2. ✓
  Calculate y $y + 10 x = 18 0^{\circ}$ (Angles on straight line)
  $y = 18 0^{\circ} - 13 0^{\circ} = 5 0^{\circ}$
  1 mark · Use angles on a straight line
3. ✓
  Calculate z $z = 7 8^{\circ}$ (Corresp $∠$ s, $ST ∥ A B$ )
  1 mark · Use angles on parallel lines
4. Question 4.1.1 · March 2021 · Provincial · 3 marks
4.1 In the diagram below, $\hat{E} = 2 x$ , $\hat{C}_{1} = 7 5^{\circ}$ , $\hat{C}_{2} = 2 x - 1 5^{\circ}$ and $\hat{B}_{2} = 13 5^{\circ}$ .
4.1.1 Determine the value of x.(3)
Show the memo (3 ticks)Memo
1. ✓
  Statement $\hat{B}_{2} = \hat{E} + \hat{C}_{1}$ , so $13 5^{\circ} = 2 x + 7 5^{\circ}$
  1 mark · Use exterior angle of a triangle
2. ✓
  Reason(ext $∠$ of $△$ )
  1 mark · Use exterior angle of a triangle
3. ✓
  Answer $2 x = 6 0^{\circ} ⟹ x = 3 0^{\circ}$
  1 mark · Use exterior angle of a triangle
5. Question 5.1 · March 2021 · Provincial · 2 marks
5.1 The angles of a certain quadrilateral are in the ratio 2:3:4:6. Calculate the size of the largest angle.(2)
Show the memo (2 ticks)Memo
1. ✓
  $x$ value $2 x + 3 x + 4 x + 6 x = 36 0^{\circ}$ (Sum of $∠$ s in quad)
  $15 x = 36 0^{\circ} ⟹ x = 2 4^{\circ}$
  1 mark · Use angle sum of a polygon
2. ✓
  Answer $6 (2 4^{\circ}) = 14 4^{\circ}$
  1 mark · Use angle sum of a polygon

Euclidean Geometry Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Grade 8: Angles on a straight line (Geometry of straight lines)Mrs Le Roux - Maths

Gr 9 Geometry: Parallel linesKevinmathscience

Finding the Missing Angle of a Triangle: A Step-by-Step GuideMath with Mr. J

Finding Missing Angles in Isosceles Triangles | Problem Solving Using Geometric RelationshipsKyle Pearce

Gr 9 Geometry: ParallelogramKevinmathscience

Interior Angles of a Polygon - GeometryThe Organic Chemistry Tutor

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