Grade 11 Maths · Euclidean Geometry · Paper 2

Lines and Triangles Grade 11

Real Lines and Triangles past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 37 past paper questions
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Question 3.7 · November 2025 · Paper 2 · Provincial · 4 marks

In the diagram, W

(1; 6)

, V, S and Q are the vertices of a quadrilateral WVSQ. P

(0; 2)

is the point where line PQ intersects the

y

-axis and R

(3; 0)

is the point where line QR intersects the

x

-axis. WV

∥

QS and WU

=

UV. PQRO is a rectangle. $Diagram for this question$

3.7 Calculate the size of

W \hat{U} Q

.(4)

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

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More Lines and Triangles Grade 11 questions and answers

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4. Question 4.2.2 · June 2024 · Paper 2 · Provincial · 2 marks
4.2 In the given figure, $D \hat{C} O = 2 5^{\circ}$ , $O$ is the center of the circle. $A$ , $B$ , $E$ , $C$ and $D$ are points on the circumference. Calculate with reasons, the size of:
4.2.2 $\hat{O}_{1}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S $\hat{O}_{1} = 2 5^{\circ} + 2 5^{\circ} = 5 0^{\circ}$
  1 mark · Use exterior angle of a triangle
2. ✓
  Rext $∠$ of $△$
  1 mark · Use exterior angle of a triangle
5. Question 1.4 · June 2024 · Paper 2 · Provincial · 2 marks
$PQRS$ is a quadrilateral with vertices $P (- 5; 0)$ , $Q (0; t)$ , $R (3; - 2)$ and $S (- 2; - 5)$ .
$P$ is on the x-axis and $Q$ is on the y-axis.
1.4 Determine the gradient of $PQ$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution into the gradient formula $m_{PQ} = \frac{3 - 0}{0 + 5}$
  1 mark · Calculate gradient between two points
2. ✓
  Gradient of PQ $m_{PQ} = \frac{3}{5}$
  1 mark · Calculate gradient between two points
6. Question 2.1 · June 2024 · Paper 2 · Provincial · 2 marks
In the diagram below, $A (- 2; 4)$ , $B (- 2; - 1)$ and $C (p; - 4)$ are the vertices of $Δ A BC$ . $Q$ is the x-intercept of the line $A C$ .
$θ$ is the angle of inclination of $A C$ and $B \hat{A} C = 3 7^{\circ}$ .
2.1 Determine the size of $θ$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Method $θ = 9 0^{\circ} + 3 7^{\circ}$ (exterior angle of a triangle)
  1 mark · Use exterior angle of a triangle
2. ✓
  Answer $θ = 12 7^{\circ}$
  1 mark · Use exterior angle of a triangle
7. Question 7.2 · November 2024 · Paper 2 · Provincial · 3 marks
In the diagram, VP $=$ PQ $= 5$ units, R $\hat{Q}$ P $=$ S $\hat{P}$ V $= α$ , S $\hat{P}$ R $= β$ and PS $∥$ QR. SV is perpendicular to VP. $Diagram for this question$
7.2 Determine RP in terms of $α$ and $β$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  P $\hat{R}$ Q $= β$ P $\hat{R}$ Q $= β$ (alt $∠$ s; RQ $∥$ SP)
  1 mark · Use angles on parallel lines
2. ✓
  Application of sine rule $\frac{s i n α}{RP} = \frac{s i n β}{5}$
  1 mark · Use the sine rule
3. ✓
  AnswerRP $= \frac{5 s i n α}{s i n β}$
  1 mark · Use the sine rule
8. Question 9.3 · November 2024 · Paper 2 · Provincial · 4 marks
In the diagram, PQRS is a cyclic quadrilateral. QA intersects SR at point A. S $\hat{A}$ Q $= 130°$ and A $\hat{Q}$ R $= 20°$ . $Diagram$
9.3 Calculate, giving reasons, the size of $\hat{P}$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  METHOD 1: S $\hat{A}_{1} = 50°$ [ $∠$ s on a str. line]
  1 mark · Use angles on a straight line
2. ✓
  METHOD 1: S $\hat{R} = 110°$ [ $∠$ s in a $Δ$ ]
  1 mark · Use angle sum of a triangle
3. ✓
  METHOD 1: S $\hat{P} = 70°$
  1 mark · Use angles of a cyclic quadrilateral
4. ✓
  METHOD 1: R[opp $∠$ s of a cyclic quad]
  1 mark · Use angles of a cyclic quadrilateral
9. Question 3.4 · November 2024 · Paper 2 · Provincial · 4 marks
In the figure quadrilateral KLMN with vertices K(7 ; -2), L(0 ; -3), M(8 ; -9) and N(9 ; -6) are given. Extend NK to intersect the $x$ -axis and form the angle $β$ .
Extend LK to intersect the $x$ -axis and form the angle $θ$ . $Diagram for this question$
3.4 Calculate the size of $α$ .(4)
Show the memo (4 ticks)Memo
1. ✓
  $m_{K L}$ $m_{K L} = \frac{- 2 - ( - 3 )}{7 - 0}$
  $m_{K L} = \frac{1}{7}$
  1 mark · Calculate gradient between two points
2. ✓
  $tan θ$ $tan θ = \frac{1}{7}$
  1 mark · Calculate the inclination of a line
3. ✓
  $θ$ $θ = 8, 13°$
  1 mark · Calculate the inclination of a line
4. ✓
  Answer $α$ $α = 116, 57° - 8, 13°$ [ext $∠$ of $Δ$ ]
  $α = 108, 44°$
  1 mark · Use exterior angle of a triangle
10. Question 10.1 · November 2024 · Paper 2 · Provincial · 6 marks
The circle is given below with TQA as a tangent. PS = SR and PQ = PR. $PQ ∥ SR$ .
SR is extended to A. $\hat{Q}_{1} = x$ and $\hat{Q}_{3} = y$ . $Diagram for this question$
10.1 Give, with reasons, THREE angles equal to $y$ .(6)
Show the memo (6 ticks)Memo
1. ✓
  S: $\hat{P}_{2} = y$ $\hat{P}_{2} = y$
  1 mark · Use the tan-chord theorem
2. ✓
  R: tan chord theorem[tangent chord theorem]
  1 mark · Use the tan-chord theorem
3. ✓
  S: $\hat{R}_{1} = y$ $\hat{R}_{1} = y$
  1 mark · Use angles on parallel lines
4. ✓
  R: alt $∠$ s[alt $∠$ s; SR//PQ]
  1 mark · Use angles on parallel lines
5. ✓
  S: $\hat{P}_{1} = y$ $\hat{P}_{1} = y$
  1 mark · Use isosceles triangle properties
6. ✓
  R: $∠$ s opp equal sides[ $∠$ s opp equal sides]
  1 mark · Use isosceles triangle properties

Lines and Triangles Grade 11 videos

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

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

Exterior Angle Theorem For Triangles, Practice Problems - GeometryThe Organic Chemistry Tutor

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