### 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 angle is an angle inside the shape.
An exterior angle is an angle outside the shape.
The sum of the three interior angles of a triangle always add up to 180 degrees.

11) 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.

12) 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

13) Can you describe the Perimeter of a shape ?
The total length of all the sides.
It is measured in mm, cm, m or km.

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) Can you give some examples of some polygons ?
Triangle - 3 sides
Pentagon - 5 sides
Hexagon - 6 sides
Heptagon - 7 sides
Octagon - 8 sides
Nonagon - 9 sides
Decagon - 10 sides

16) 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.

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

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

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

20) How many different types of Quadralateral are there ?
Kite - 2 pairs of equal sides, 1 pair equal angles
Rhombus - 4 equal length sides, 2 pairs equal angles (special type of Kite)
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)

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

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

23) How many different types of Triangle are there ?
Scalene - 3 sides and angles are all different
Equalateral - 3 sides and angles are all equal
Isosceles - 2 sides and 2 angles equal

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

25) What is a Right Angled Triangle ?
Is a triangle with one right angle.

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

27) How do we measure Area ?
By multiplying the length and the width.
The units of area are square units, cm2 or m2

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

29) Can you calculate the Area of a Triangle ?

30) Can you calculate the Area of a Parallelogram ?

31) Can you calculate the Area of a Trapezium ?

32) 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.

33) Can you describe Rotational Symmetry ?
When it still looks the same after some rotation (of less than one full turn).
The number of times it matches as we around is called the order.

34) 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

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

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

37) 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.

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

39) 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.

40) What is the Circumference of a Circle ?
This is the name for the perimeter of a circle.
It is the distance all the way around.

41) What is the Radius of a Circle ?
The distance from the center of the circle to any point on its circumference.

42) What is the Diameter of a Circle ?
The distance straight across a circle going through the centre.
It is two times the radius.

43) Can you calculate the Area of a circle ?

44) Can you calculate the Circumference of a circle ?

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

46) What is a Chord ?
A line drawn across the inside of a circle.

47) What is an Arc ?
An arc is part of the circumference of a circle.

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

49) What is a Segment ?
A segment is the area you get when you cut through a circle along a chord.

50) 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

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

52) What is a Vertex ?
This is a corner/point where two or more edges meet.

53) 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.
Cone - Has a circular base and tapers up to a single point called the apex.
Cylinder - Has a circular or oval cross-section. Has three faces.
Triangular Prism - Has five faces, two triangular bases and three rectangular faces.
Square Prism - (Cube) - Has six faces that are all squares.
Rectangular Prism - (Cuboid) - Has six faces that are all rectangles and the opposite faces are equal.
Triangular Based Pyramid - Has four faces that are all triangles. (Tetrahedron, regular or irregular).
Square Based Pyramid - Has five faces, one square and four triangles.

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

55) How many edges, faces and vertices does a Triangular Based Pyramid have ?
Faces - 4
Edges - 6
Vertices - 4

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

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

58) 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.

59) What is a Cuboid ?
A rectangular prism that has 6 faces.

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

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

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

63) 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.

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

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

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

67) What is a Octahedron ?
This is a polyhedron with 20 faces.

68) What is a Icasahedron ?
This is a polyhedron with 8 faces.

69) 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.

70) How do we measure Surface Area ?
Surface Area only applies to 3D shapes.
It is the total area of all the faces added together.

71) Can you calculate the surface area of a Cylinder ?

72) How do we measure Capacity ?
The capacity of a container is how much water (or liquid) it will hold.
It is measured in millimeters (ml) or litres (l).

73) How do we measure Volume ?
The amount of space a 3D shape takes up.
It is measured in cubic centimeters (cm3) or cubic metres (m3).

74) What does Fill mean ?

75) Can you calculate the volume of a Box or Cuboid ?
length x height x width

76) Can you calculate the volume of a Prism ?

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