Special Properties, SMB-025
A quadrilateral is pictured below.
What is the value of `x`? (3 marks)
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Special Properties, SMB-026
A pentagon is pictured below, where one internal angle is a right angle.
What is the value of `x`? (3 marks)
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Special Properties, SMB-024
A quadrilateral is drawn below.
What is the value of `x`? (3 marks)
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Special Properties, SMB-030
Special Properties, SMB-029
A regular nonagon is pictured below.
What is the value of `x`? (2 marks)
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Special Properties, SMB-028
Special Properties, SMB-027
A regular pentagon is pictured below.
What is the value of `x`? (2 marks)
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Special Properties, SMB-024
A quadrilateral is drawn below.
What is the value of `x`? (3 marks)
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Special Properties, SMB-023
A pentagon is drawn below.
What is the value of `x`? (3 marks)
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Special Properties, SMB-022
A quadrilateral is drawn below.
What is the value of `x`? (2 marks)
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Special Properties, SMB-021
A five sided polygon is drawn below.
What is the value of `x`? (2 marks)
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Congruency, SMB-016
Special Properties, SMB-020 MC
`AB` is the diameter of a circle, centre `O`.
There are 3 triangles drawn in the lower semi-circle and the angles at the centre are all equal to `x^@`.
The three triangles are best described as:
- isosceles
- scalene
- right-angled
- equilateral
Special Properties, SMB-019
Special Properties, SMB-018
Special Properties, SMB-017
Special Properties, SMB-016
Special Properties, SMB-015
Special Properties, SMB-014
Special Properties, SMB-012
Special Properties, SMB-013 MC
Which statement is always true?
- Scalene triangles have two angles that are equal.
- All angles in a parallelogram are equal.
- The opposite sides of a trapezium are equal in length.
- The diagonals of a rhombus are perpendicular to each other.
Special Properties, SMB-011 MC
Special Properties, SMB-010 MC
Which of these are always equal in length?
- the diagonals of a rhombus
- the diagonals of a parallelogram
- the opposite sides of a parallelogram
- the opposite sides of a trapezium
Special Properties, SMB-009 MC
Special Properties, SMB-008
Special Properties, SMB-007 MC
A closed shape has two pairs of equal adjacent sides.
What is the shape?
- rectangle
- trapezium
- kite
- triangle
Special Properties, SMB-006
Congruency, SMB-013
Which two of the triangles below are congruent? (2 marks)
Congruency, SMB-012
Which two of the triangles below are congruent? (2 marks)
Congruency, SMB-015
Special Properties, SMB-005 MC
`A`, `B` and `C` are vertices on the cube below.
What is the best description of `DeltaABC`?
- isosceles
- equilateral
- scalene
- right-angled
Congruence, SMB-014
Special Properties, SMB-004 MC
Which one of the following triangles is impossible to draw?
- a right angled triangle with two acute angles
- an isosceles triangle with one right angle
- a scalene triangle with three acute angles
- a right angled triangle with one obtuse angle
Special Properties, SMB-003 MC
Special Properties, SMB-002 MC
A triangle has two acute angles.
What type of angle couldn't the third angle be?
- an acute angle
- an obtuse angle
- a right-angle
- a reflex angle
Special Properties, SMB-001 MC
Which of the following triangle types is impossible to draw?
- a right-angled, scalene triangle
- a right-angled, equilateral triangle
- an obtuse-angled, isosceles triangle
- an acute-angled, scalene triangle
Congruency, SMB-011
The diagram shows a circle with centre `O` and radius 5 cm.
The length of the arc `PQ` is 9 cm. Lines drawn perpendicular to `OP` and `OQ` at `P` and `Q` respectively meet at `T`.
Prove that `Delta OPT` is congruent to `Delta OQT`. (2 marks)
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Congruency, SMB-010
In the diagram, `AD` is parallel to `BC`, `AC` bisects `/_BAD` and `BD` bisects `/_ABC`. The lines `AC` and `BD` intersect at `P`.
- Prove that `/_BAC = /_BCA`. (1 mark)
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- Prove that `Delta ABP ≡ Delta CBP`. (2 marks)
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Similarity, SMB-028
The floor plan of a home unit has been drawn to scale.
What is the total floor area of the home unit in square metres? (2 marks)
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Similarity, SMB-027
- What scale factor is used to convert Circle A into Circle B. (1 mark)
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- Complete this equation:
- Area of Circle A = _____ × Area of Circle B. (1 mark)
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Congruency, SMB-008
In the figure below, \(ABCD\) is a parallelogram where opposite sides of the quadrilateral are equal.
Prove that a diagonal of the parallelogram produces two triangles that are congruent. (2 marks)
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Congruency, SMB-007
In the figure below, \(AB \parallel DE, \ AC = CE\) and the line \(AE\) intersects \(DB\) at \(C\).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-006
In the quadrilateral \(ABCD\), \(AB \parallel CD, \angle BAD = \angle BCD\) and \(\angle DBC = \angle BDA = 90^{\circ} \).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-005
In the figure below, \(BE = BC\), \(AB = BD\) and the line \(AD\) intersects \(CE\) at \(B\).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-004
In the circle below, centre \(O\), \(OB\) is perpendicular to chord \(AC\).
Prove that a pair of triangles in this figure are congruent. (2 marks)
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Congruency, SMB-003
In the figure below, the line \(AD\) intersects \(BE\) at \(C\), \(BC = CD\) and \(AC = EC\).
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-002
The diagram shows two triangles that touch at the middle of a circle.
Prove that this pair of triangles are congruent. (2 marks)
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Congruency, SMB-001
The diagram shows two right-angled triangles where \(\angle BAC = \angle BDC = 90^{\circ}\), and \(AB = BD\).
Prove that this pair of triangles are congruent. (2 marks)
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Similarity, SMB-026
The two triangles below are similar.
Find the length of \(ED\). (3 marks)
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Similarity, SMB-025
A triangular prism is pictured below.
By what factor will its volume change if
- Each dimension is doubled? (1 mark)
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- Each dimension is decreased by two-thirds? (2 marks)
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Similarity, SMB-024
Prove that the two triangles in the right cone pictured below are similar. (2 marks)
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Similarity, SMB-023
Show that \(\Delta ACD\) and \(\Delta DCB\) in the figure below are similar. (2 marks)
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Similarity, SMB-022
Similarity, SMB-021
Prove that this pair of triangles are similar. (2 marks)
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Similarity, SMB-020
Prove that this pair of triangles are similar. (3 marks)
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Similarity, SMB-019
Prove that this pair of triangles are similar. (2 marks)
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Similarity, SMB-018
Prove that this pair of triangles are similar. (2 marks)
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Similarity, SMB-017
Prove that this pair of triangles are similar. (2 marks)
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Congruency, SMB-009
The diagram shows a right-angled triangle `ABC` with `∠ABC = 90^@`. The point `M` is the midpoint of `AC`, and `Y` is the point where the perpendicular to `AC` at `M` meets `BC`.
Show that `\Delta AYM \equiv \Delta CYM`. (2 marks)
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