Grade 10 Maths · Euclidean Geometry

Use properties of quadrilaterals

Use the facts about a shape's sides, angles and diagonals to find something (for example opposite sides of a parallelogram are equal).

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Question 5.2 · March 2020 · Provincial · 4 marks

Euclidean Geometry calculations:

5.2 PQRS is a parallelogram.

PT = 4 x - 2

TR = x + 28

ST = 4 y - 7

and

TQ = y + 14

. Determine x and y.(4) Diagram for question 5.2

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

More past paper questions: use properties of quadrilaterals

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3. Question 4.2.1 · March 2022 · Provincial · 2 marks
4.2 EFGH is a rhombus in which the diagonals EG and FH intersect at M. $F \hat{E} H = 10 0^{\circ}$ . Find the value of:
4.2.1 $F \hat{E} M$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Statement (S) $F \hat{E} M = 5 0^{\circ}$
  1 mark · Use properties of quadrilaterals
2. ✓
  Reason (R)Diagonals of a rhombus bisect the vertex $∠$ s
  1 mark · Use properties of quadrilaterals
4. Question 6.1.3 · March 2020 · Provincial · 3 marks
Proofs and Geometry problems:
6.1 JKLM is a rectangle. MLPR is a rhombus. $J \hat{M} K = R \hat{M} P = 5 5^{\circ}$ and $M \hat{R} P = 7 0^{\circ}$ . Determine:
6.1.3 $K \hat{L} P$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Identify components $M \hat{L} K = 9 0^{\circ}$ (rect property) \n $M \hat{L} P = 180 - (55 + 55) = 7 0^{\circ}$ (opp $∠$ s rhombus equal)
  2 marks · Use properties of quadrilaterals
2. ✓
  Add components $K \hat{L} P = 9 0^{\circ} + 7 0^{\circ} = 16 0^{\circ}$
  1 mark · Use properties of quadrilaterals
5. 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
6. Question 8.1.2 · 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:
8.1.2 $C \hat{E} B = A \hat{F} D$ (3)
Show the memo (3 ticks)Memo
1. ✓
  S/R: Ĉ₁ = Â₂ $\hat{C}_{1} = \hat{A}_{2}$ (alt $∠$ s; $BC ∥ A D$ )
  1 mark · Use angles on parallel lines
2. ✓
  S/R: B̂ = D̂ $\hat{B} = \hat{D}$ (opp $∠$ s of parm) | $\hat{B}_{1} = \hat{D}_{1}$ (proven, $Δ A BE \equiv Δ C D F$ )
  1 mark · Use properties of quadrilaterals
3. ✓
  S/R: B̂₂ = D̂₂ $\hat{B}_{2} = \hat{D}_{2}$ | $∴ \hat{E}_{2} = \hat{F}_{2}$ (sum of $∠$ s of $Δ$ ), i.e. $C \hat{E} B = A \hat{F} D$
  1 mark · Use angle sum of a triangle

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