Grade 10 Maths · Euclidean Geometry · Paper 2

Lines, Angles and Triangles Grade 10

Real Lines, Angles and Triangles 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: 64 past paper questions
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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.

Lines, Angles and Triangles skills

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More Lines, Angles and Triangles Grade 10 questions and answers

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4. 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
5. Question 10.2.4 · November 2024 · Paper 2 · Provincial · 2 marks
10.2 In the diagram, PAT is the common tangent of the smaller and larger circles at A. AMB is the diameter of the larger circle with M on the circumference of the smaller circle. ASC and BC are chords of the larger circle and MS chord of the smaller circle. M is the centre of the larger circle.

It is also given that, the length of AM $= p$ units, AS $= (p - 1)$ units and BC $= 6$ units.

Answer the questions that follow. $Diagram for question 10.2$
10.2.4 Write down the length of MS with a reason.(2)
Show the memo (2 ticks)Memo
1. ✓
  SMS $= 3$
  1 mark · Use the mid-point theorem
2. ✓
  R[midpoint theorem]
  1 mark · Use the mid-point theorem
6. Question 8.1 · November 2024 · Paper 2 · Provincial · 3 marks
A mine dumps its waste at a landfill site where it takes the shape of a cone shown in the diagram below. The radius of the circular base is $r$ meters, the height is $h$ meters and the angle between the slant height and the base of the cone is $50°$ .
The circumference of the landfill site is 245 meters.

Volume of cone $= \frac{1}{3} π r^{2} h$

Total surface area of cone $= π r^{2} + π rs$ $Diagram for this question$
8.1 Determine the height of the mine waste, correct to ONE decimal place.(3)
Show the memo (3 ticks)Memo
1. ✓
  $r = 39$ m $2 π r = 245$
  $∴ r = \frac{245}{2 π}$
  $r = 39$ m
  1 mark · Calculate area or perimeter
2. ✓
  $\frac{h}{r} = tan 50°$ In $Δ A BC$ : $\frac{h}{r} = tan 50°$
  1 mark · Calculate a side using trig
3. ✓
  Answer $∴ h = 39. tan 50°$
  $∴ h = 46, 5$ m
  1 mark · Calculate a side using trig
7. Question 4.1 · March 2022 · Provincial · 5 marks
4.1 Find the values of x, y and z in the diagram below. Give a reason for each statement.(5)
Show the memo (5 ticks)Memo
1. ✓
  x with reason (S & R) $x = 3 4^{\circ}$ (Corresponding $∠$ s, lines parallel)
  1 mark · Use angles on parallel lines
2. ✓
  Solve for y $y = 7 8^{\circ}$ (Alternate $∠$ s, lines parallel)
  1 mark · Use angles on parallel lines
3. ✓
  Statement for z (S) $z = 18 0^{\circ} - (3 4^{\circ} + 7 8^{\circ}) = 18 0^{\circ} - 11 2^{\circ}$
  1 mark · Use angle sum of a triangle
4. ✓
  Reason (R)Sum of $∠$ s in $Δ$
  1 mark · Use angle sum of a triangle
5. ✓
  Answer $z = 6 8^{\circ}$
  1 mark · Use angle sum of a triangle
8. 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
9. 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
10. 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

Lines, Angles and Triangles 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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