In the diagram,
- Show that the size of
is 108°. (1 mark)
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- Find the size of
. Give reasons for your answer. (2 marks)
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ii.
Special Properties, SMB-025
A quadrilateral is pictured below.
What is the value of
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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
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Special Properties, SMB-024
A quadrilateral is drawn below.
What is the value of
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Special Properties, SMB-030
A regular decagon is pictured below.
- What is the value of
? (2 marks)
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- What is the size of an internal angle of a decagon? (2 marks)
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Special Properties, SMB-029
A regular nonagon is pictured below.
What is the value of
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Special Properties, SMB-028
A regular hexagon is pictured below.
What is the value of
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Special Properties, SMB-027
A regular pentagon is pictured below.
What is the value of
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Special Properties, SMB-024
A quadrilateral is drawn below.
What is the value of
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Special Properties, SMB-023
A pentagon is drawn below.
What is the value of
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Special Properties, SMB-022
A quadrilateral is drawn below.
What is the value of
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Special Properties, SMB-021
A five sided polygon is drawn below.
What is the value of
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Congruency, SMB-016
Special Properties, SMB-020 MC
There are 3 triangles drawn in the lower semi-circle and the angles at the centre are all equal to
The three triangles are best described as:
- isosceles
- scalene
- right-angled
- equilateral
Special Properties, SMB-019
A regular pentagon, a square and an equilateral triangle meet at a point.
What is the size of the angle
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Special Properties, SMB-018
Special Properties, SMB-017
Special Properties, SMB-016
Two identical quadrilaterals fit together to make this regular pentagon.
What is the value of
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Special Properties, SMB-015
Special Properties, SMB-014
The sum of the interior angles of a 6 sided polygon can be found by first dividing it into triangles from one vertex.
What is the sum of the interior angles of this polygon? (2 marks)
Special Properties, SMB-012
What is the size of
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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
Show Worked Solution
Special Properties, SMB-009 MC
Special Properties, SMB-008
The sum of the internal angles of a polygon can be calculated by drawing triangles from any given vertex as shown below.
What is the size of the angle marked
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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
Eloise makes a sketch of the playground at her school.
What is the size of angle
Special Properties, SMB-005 MC
What is the best description of
- isosceles
- equilateral
- scalene
- right-angled
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
Plane Geometry, 2UA 2004 HSC 2b
In the diagram,
Find the size of
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Plane Geometry, 2UA 2005 HSC 5b
The diagram shows a parallelogram
Prove that
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Plane Geometry, 2UA 2008 HSC 4a
In the diagram,
Prove that
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Plane Geometry, 2UA 2011 HSC 6a
The diagram shows a regular pentagon
- Find the size of
. (1 mark)
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- Hence, show that
is isosceles. (2 marks)
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MARKER’S COMMENT: Very few students solved part (i) efficiently. Remember the general formula for the sum of internal angles equals (# sides – 2) x 90°.
ii.