Grade 10 Maths · Euclidean Geometry

Use angles on parallel lines

Find angles when a line crosses parallel lines, using alternate, corresponding or co-interior angles, or use such angles to show two lines are parallel.

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Gr 9 Geometry: Parallel linesKevinmathscience

How to Calculate ANGLES on Parallel Lines - GEOMETRY 101 - Grade 8SHFT - Your Learning

Grade 8: Alternate angles (parallel lines)Mrs Le Roux - Maths

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Question 7.2 · March 2022 · Provincial · 2 marks

In the diagram,

A C

and

CE

are tangents to the circle with centre

O

B, D, G

and

H

are points on the circumference.

H G

is produced to

F

B D = B H

\hat{D}_{1} = \hat{D}_{4} = x

7.2 Hence or otherwise prove that

B D ∥ H G

.(2)

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More past paper questions: use angles on parallel lines

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3. Question 5.2.1(b) · June 2024 · Paper 2 · Provincial · 2 marks
5.2 In the diagram below, $O$ is the centre of the circle and $A C$ is the diameter.
$A C$ is produced to meet $E D$ produced at $G$ . $OE ∥ C D$ and $\hat{B} = 7 2^{\circ}$ .
5.2.1 Calculate, giving reasons, the size of:
5.2.1(b) $\hat{O}_{1}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Statement $\hat{O}_{1} = \hat{C}_{1} = 7 2^{\circ}$
  1 mark · Use angles on parallel lines
2. ✓
  Reason(corresponding angles, $OE ∥ C D$ )
  1 mark · Use angles on parallel lines
4. Question 5.2.3 · June 2024 · Paper 2 · Provincial · 3 marks
ABCD is a rhombus with the diagonals $A C = 16$ cm and $D B = 30$ cm.
5.2 Calculations involving the rhombus properties.
5.2.3 Determine the size of $O \hat{B} F$ if $O \hat{F} C = 6 4^{\circ}$ .(3)
Show the memo (2 ticks)Memo
1. ✓
  Find angle B (total) $O \hat{F} C = \hat{B}_{1} + \hat{B}_{2}$ (Corresponding angles, AB || OF)
  Or $\hat{C}$ interior angles...
  2 marks · Use angles on parallel lines
2. ✓
  Bisect angle $\hat{B}_{1} = \hat{B}_{2}$ (Diagonals of rhombus bisect angles)
  $O \hat{B} F = \frac{6 4 ^{\circ}}{2} = 3 2^{\circ}$
  1 mark · Use properties of quadrilaterals
5. Question 8.1.3 · November 2024 · Paper 2 · Provincial · 3 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:
8.1.3 $A F = CE$ (3)
Show the memo (3 ticks)Memo
1. ✓
  S/R: Ĉ₁ = Â₂In $Δ CBE$ and $Δ A D F$ : | $\hat{C}_{1} = \hat{A}_{2}$ (proven / alt $∠$ s; $BC ∥ A D$ )
  1 mark · Use angles on parallel lines
2. ✓
  S/R: B̂₂ = D̂₂ $\hat{B}_{2} = \hat{D}_{2}$ (proven in 8.1.2)
  1 mark · Use angles on parallel lines
3. ✓
  Conclusion $BC = A D$ (opp sides of parm) | $∴ Δ CBE \equiv Δ A D F$ (AAS) | $∴ A F = CE$ (congruent $Δ$ s)
  1 mark · Prove triangles congruent
6. Question 4.1.2 · 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 $\hat{B}_{2} = 13 5^{\circ}$ .
4.1.2 Determine if $EF ∥ G H$ . Motivate your answer.(3)
Show the memo (3 ticks)Memo
1. ✓
  Calculate C2 $\hat{C}_{2} = 2 (3 0^{\circ}) - 1 5^{\circ} = 4 5^{\circ}$
  1 mark · Substitute into a formula
2. ✓
  Statement $\hat{B}_{2} + \hat{C}_{2} = 13 5^{\circ} + 4 5^{\circ} = 18 0^{\circ}$
  1 mark · Use angles on parallel lines
3. ✓
  ReasonYes, $EF ∥ G H$ (Co-interior angles supplementary)
  1 mark · Use angles on parallel lines

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