# Questions - Geometry

1) What is Geometry ?
This is all about shapes and their properties.

2) What does intersect mean ?
Intersect means meet.

3) What are intersecting lines ?
They are two lines that meet at one point.
Two intersecting lines always form a plane.

4) What are parallel lines ?
They are two lines that are always the same distance apart, they never meet.
They do not have to be straight lines (eg railway tracks).

5) What are perpendicular lines ?
Two lines that are at right angles to one another.
We say one line is perpendicular to the other.

6) What is an Angle ?
An angle is the space between two intersecting lines.
An angle tells us how far something turns or rotates.

7) What is a Right Angle ?
A right angle is an internal angle which is equal to 90 degrees.

8) How do we measure angles ?
Angles can be measured using a protractor.
The size of an angle is measured in degrees.

9) How many different types of angles are there ?
Acute - Less than a right angle less than 90
Right Angled - 90 degrees
Obtuse - Greater than 90 degrees (right angle) but less than 180 degrees
Straight - 180 degrees
Reflex - Greater than 180 degrees

10) What is the difference between an Interior and an Exterior angle ?
An interior (or internal) angle is an angle inside the shape.
An exterior (or external) angle is an angle outside the shape.

11) What does the sum of the interior angles of a triangle add up to ?
The sum of the three interior angles of a triangle always add up to 180 degrees.

12) What is the 3 Letter Angle Notation ?
We can name angles using three capital letters <ABC
The middle letter is called the vertex of the angle.

13) What are the 6 rules of Geometry ?
Angles in a triangle add up to 180 degrees
Angles on a straight line add up to 180 degrees
Angles around a point add up to 360 degrees
Exterior angles of a triangle equals the sum of the opposite interior angles
Isosceles triangles have 2 sides and 2 angles equal

14) What is the definition of a Polygon ?
Any 2D flat shape that is made up of straight lines called sides.
A circle is not a polygon.

15) What Properties do 2D shapes have ?
Sides - These are the straight lines
Angles - The space between the 2 intersecting lines
Corners - (vertex) Where two sides meet to make an angle

16) Can you give some examples of some polygons ?
These can all be regular or irregular.
Triangle - 3 sides
Pentagon - 5 sides
Hexagon - 6 sides
Heptagon - 7 sides
Octagon - 8 sides
Nonagon - 9 sides
Decagon - 10 sides
Dodecagon - 12 sides
Icosagon - 20 sides (eye-co-sagon)

17) What is a Regular Polygon ?
A polygon is called regular when all the sides are the same length and all the angles are the same size.
A regular polygon with 3 sides = equalateral triangle
A regular polygon with 4 sides = square

18) What is an Irregular Polygon ?
A polygon that does not have all its sides and angles equal.

19) Can you draw an irregular polygon ?

20) Can you draw an irregular pentagon ?

21) What is a Diagonal ?
A diagonal is a line connecting two corners (or vertices) of a Polygon

22) How many diagonals does a Hexagon have ?
A polygon with N sides will have N(N-3) / 2 diagonals
There are 9.

23) What is a Line of Symmetry ?
The line on which a mirror can be placed to show the reflection of a 2D shape.

24) How many different types of Quadrilateral are there ?
Kite - 2 pairs of equal sides, 1 pair equal angles, 1 line of symmetry
Rhombus - 4 equal length sides, 2 pairs equal angles (special type of Kite), 2 lines of symmetry
Trapezium - 1 pair parallel sides
Parallelogram - 2 pairs equal sides, 2 pairs equal angles, 2 pairs parallel sides
Rectangle - 2 pairs equal sides, all angles are right angles
Square - 4 equal sides, all anles are right angles (special type of rectangle)

25) What is the difference between a Kite and a Rhombus ?
A kite does not have 4 equal sides.
A kite only has 1 line of symmetry.

26) What is the difference between a Rhombus and Parallelogram ?
A parallelogram has opposite sides equal in length.
A rhombus has all four sides equal in length.

27) Which shape has exactly one pair of parallel sides ?
Trapezium

28) Are the following True or False ?
A square is a special type of rectangle - True
A rhombus is a square pushed to the side - True
A rhombus is a special type of parallelogram - True
A rhombus is a special type of kite - True

29) Is a Diamond a shape ?
Yes. It is an example of a rhombus

30) How many different types of Triangle are there ?
Scalene - 3 sides and angles are all different
Equalateral - 3 sides and angles are all equal. Also called a Regular Triangle
Isosceles - 2 sides and 2 angles equal

31) What is a Right Angled Triangle ?
Is a triangle with one 90 degree angle.
It could be scalene or an isosceles triangle.

32) What is an Acute-Angled Triangle ?
Is a triangle with three acute angles.

33) What is an Obtuse-Angled Triangle ?
Is a triangle with one obtuse angle.

34) Can you describe Line Symmetry ?
It cuts a 2D shape into two halves.
One half is the reflection of the other half.
Divides it into identical halves.
Draw all the capitals letters and mark on any lines of symmetry.

35) How many lines of symmetry do these 2D shapes have ?
Regular Pentagon - 5
Regular Hexagon - 6
Regular Octagon - 8

36) Can you describe Rotational Symmetry ?
Rotational symmetry is when you turn a shape round its centre and it fits exactly on top of itself.
When it still looks the same after some rotation (of less than one full turn).
The number of times it does this is called the order of symmetry.

37) How many different types of Transformation are there ?
Translation - moving the shape left, right, up or down
Reflection - reflecting the shape in a mirror
Rotation - turning the shape round a point
Enlargement - all the distances from the centre of enlargement are multiplied by the scale factor

38) If two 2D shapes are Congruent what does that mean ?
They are the same shape and the same size.

39) If two 2D shapes are Similar what does that mean ?
They have the same interior angles.

40) What are Convex and Concave Shapes ?
Convex shapes have no internal angles greater than 180 degrees.
Concave shapes have at least one internal angle greater than 180 degrees.

41) What is the Perimeter of a 2D shape ?
The distance all the way around the outside of a 2D shape.

42) Does a Circle have a side ?
No. It is made up of arcs creating a continuous line that meets at two ends.
A side must be comprised of a line and two angles, one of each side of the line.

43) Circles - What is the Circumference ?
This is the name for the perimeter of a circle.
It is the distance all the way around.

44) Circles - What is the Radius ?
The distance from the center of the circle to any point on its circumference.

45) Circles - What is the Diameter ?
The distance straight across a circle going through the centre.
It is two times the radius.

46) Circles - How do you calculate the circumference of a circle ?
C = Pi x Diameter
C = 2 x Pi x Radius

47) Circles - What is Pi ?
A Greel letter that represents the constant ratio of the circumference of any circle, to its diameter.
Pi = 3.1416

48) Circles - What is the Area of a circle ?
Pi multiplied by the square of the radius.

49) Circles - What is a Tangent ?
A straight line that just touches the outside of a circle.

50) Circles - What is a Chord ?
A line drawn across the inside of a circle.

51) Circles - What is an Arc ?
An arc is part of the circumference of a circle.

52) Circles - What is a Sector ?
A sector is a wedge-shaped area cut right from the centre.

53) Circles - What is a Segment ?
A segment is the area you get when you cut through a circle along a chord.
Think of a slice of pizza.

54) Circles - What are Concentric Circles ?
These are circles that share the same centre point but have a different radius.

55) What is the Perimeter of a 2D shape ?
The total length of all the sides.
It is measured in mm, cm, m or km.

56) What is the Area of a 2D shape ?
The area of a 2D shape is the size that a surface takes up.
The area of a 2D shape is the amount of space inside it.
It is measured in "square" units of measurement.
mm2, cm2, m2, km2

57) What are the four Area Formulas ?
Area of a Rectangle
Area of a Triange
Area of a Parallelogram
Area of a Trapezium

58) Can you calculate the Area of a Rectangle ?
A = length x width 59) Can you calculate the Area of a Triangle ?
A = 1/2 x base x height

60) Can you calculate the Area of a Parallelogram ?
A parallelogram with base B and height H has the same area as a rectangle with base B and height H.
A = base x height 61) Can you calculate the Area of a Trapezium ?
a is the length of one parallel side
b is the length of the other parallel side
A = 1/2 x (a + b) x height 62) What is a Compound Shape ?
Also known as a Composite Shape.
This is a shape that is made up of two or geometric shapes.

63) What is a Geometric Shape ?
These are mathematical shapes that are regular.

64) How can we calculate the area of a composite or compound shape ?
We can partition the shape into smaller rectangles and triangles, calculate the area of these and then add them together.

65) Can you give some examples of 3D Shapes ?
Sphere - A perfectly round 3D shape, like a ball. All points on the surface are the same distance from the centre.
(1 face, 0 edges, 0 vertices)
Cone - Has a circular base and tapers up to a single point called the Apex.
(2 faces, 1 edge, 1 vertex)
Cylinder - Has a circular or oval cross-section. Has three faces.
(3 faces, 2 edges, 0 vertices)
Triangular Prism - Has five faces, two triangular bases and three rectangular faces.
Square Prism - (Cube) - Has six faces that are all squares.
(6 faces, 12 edges, 8 vertices)
Rectangular Prism - (Cuboid) - Has six faces that are all rectangles and the opposite faces are equal.
(6 faces, 12 edges, 8 vertices)
Hexagonal Prism - Has eight faces, two hexagons and six rectangles.
(8 faces, 8 edges, 12 vertices)
Triangular Based Pyramid - (Tetrahedron) Has four faces that are all triangles.
(4 faces, 6 edges, 4 vertices)
Square Based Pyramid - Has five faces, one square and four triangles.
(5 faces, 8 edges, 5 vertices)
Hexagonal Pyramid - Has seven faces, one hexagon and six triangles.
(7 faces, 12 edges, 7 vertices)

66) What Properties do 3D shapes have ?
Faces - (flat bits) a 2D shape that makes up one surface of a 3D shape
Edges - (straight lines / sides) where two faces meet
Vertices - (vertex, corners) where two or more edges meet

67) What shape has 6 rectangular faces. Not all the sides are identical ?
Rectangular Prism.

68) What is a Cuboid ?
A rectangular prism that has 6 faces.
A cuboid could have 2 square faces and 4 identical rectangular faces.
A cuboid could have 3 sets of different size rectangular faces.

69) What is a Sphere ?
A perfectly round 3D shape, like a ball. All points on the surface are the same distance from the centre.

70) Can you name a 3D shape that only has one curved face ?
Sphere.

71) How many vertices does a sphere have ?
None

72) How many faces does a cylinder have ?
Three. A cylinder has two flat faces (circles) and one curved face (rectangle)

73) Is a Cylinder a prism ?
No. Because all prisms must have flat faces and a cylinder has one curved face.

74) Is a Cone a prism ?
No. Because both ends are not the same.

75) What is a Pyramid ?
It has a polygon base and flat (triangular) sides that join at a common point called the apex.
When the base is a regular polygon it is called a regular pyramid.

76) What is the top of a Pyramid called ?
Apex - the top or highest part of something.

77) What is a Prism ?
A prism has a constant cross section.
Both ends of the 3D shape are the same.
The two end faces must be joined together using rectangles or squares.

78) What is a Polyhedron ?
Any 3D shape that has polygon faces.
No curved surfaces (cones, spheres and cylinders are not polyhedrons).

79) What is a Tetrahedron ?
A triangular based pyramid with equal sides is called a tetrahedron.
This is a polyhedron with four triangular sides.

80) What is a Octahedron ?
This is a polyhedron with 8 faces. Can you draw one. 81) What is a Icosahedron ?
This is a polyhedron with 20 faces. A dice with 20 sides.

82) What is a Net ?
A net is a hollow 3D shape folded out flat.
A net is what you would draw, cut out and fold, to make a 3D shape.

83) How many different nets does a cube have ?
11 (eleven)

84) What is Surface Area of a 3D shape ?
The surface area of a 3D shape is the total area of all its faces.
To calculate the surface area you can find the area of its net.

85) Can you calculate the surface area of a Cylinder ?
(2 x PI x Radius x height) + (2 x PI x r2)

86) What is the Volume of a 3D shape ?
Volume is the amount of space a 3D shape takes up.

87) Can you calculate the Volume of a Cuboid ?
V = length x height x width 88) Can you calculate the Volume of a Cube ?
V = length x length x length
V = length(cubed)

89) Can you calculate the Volume of a Prism ?
V = (area of base) x length

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