Two-dimensional figures
A two-dimensional figure is a figure that has length and width but no depth. Straight or curved lines make up the sides of this shape. Also, these figures can have any number of sides. In general, plane figures made of lines are known as polygons.
Examples: Circle, Triangle,Square,Rectangle,Pentagon,Octagon

Regular Polygon
If all the sides and interior angles of the polygon are equal, then it is known as a regular polygon. The examples of regular polygons are square, rhombus, equilateral triangle, etc.

Irregular Polygon
If all the sides and the interior angles of the polygon are of different measure, then it is known as an irregular polygon. For example, a scalene triangle, a rectangle, a kite, etc.

CIRCLE
A circle is a shape consisting of all points in a plane that are a given distance from a given point, the centre.The distance from the center to the outer line of the circle is called a radius. The example of the circle in real life are wheels, pizzas, orbit, etc.

The Radius is the distance from the center outwards.
The Diameter goes straight across the circle, through the center.
The Circumference is the distance once around the circle.
A line segment that goes from one point to another on the circle's circumference is called a Chord.

TRIANGLE
A triangle is a three-sided polygon (2d Shape) that has three edges and three vertices. The sum of all the three angles of a triangle is equal to 180°.

Types of triangle:

Scalene Triangle: All the sides and angles are unequal.

Isosceles Triangle: It has two equal sides. The angles opposite these equal sides are equal.

Equilateral Triangle: All the sides are equal and all the three angles equal to 60°.

Acute Angled Triangle: A triangle having all its angles less than 90°.

Right Angled Triangle: A triangle having one of the three angles exactly 90°.

Obtuse Angled Triangle: A triangle having one of the three angles more than 90°.

Triangle Properties:
The sum of all the angles of a triangle(of all types) is equal to 180°.
The sum of the length of the two sides of a triangle is greater than the length of the third side.
In the same way, the difference between the two sides of a triangle is less than the length of the third side.
The side opposite the greater angle is the longest side of all the three sides of a triangle.
The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property.

Two triangles are said to be similar if their corresponding angles of both triangles are congruent and lengths of their sides are proportional.

QUADRILATERAL
A Quadrilateral is a polygon having the number of sides equal to four. That means, a polygon formed by enclosing four line segments such that they meet at each other at corners/vertices to make 4 angles.
The quadrilaterals are Square,Rectangle,Parallelogram,Rhombus
Trapezium.

SQUARE
A square is a four-sided polygon (2d Shape), whose four sides are equal in length and all the angles are equal to 90°. The diagonals of the square also bisect each other at 90°. A wall where all the sides are equal are the examples of square.

RECTANGLE
A rectangle is a 2d shape which has four sides, where the opposite sides are equal and parallel to each other. All the angles of a rectangle are equal to 90°. A TV, cardboard, are examples of the rectangle.

RHOMBUS
A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles.

TRAPEZIUM
The trapezium is a quadrilateral with two parallel sides. The parallel sides of a trapezium are called bases and the non-parallel sides of a trapezium are called legs. It is also called a trapezoid. Sometimes the parallelogram is also called a trapezoid with two parallel sides.

PENTAGON
A pentagon is a five-sided polygon (2d Shape), and it can be regular or irregular. In the case of a regular pentagon, each interior angle is equal to 108°, and each exterior angle measures 72°. It has five diagonals.

OCTAGON
An octagon is an eight-sided polygon which can be either regular or irregular. It is a 2d shape which has eight angles. The sum of all the interior angles of an octagon is 1080°. The stop sign board has an octagon shape, which you can see on the roadside.

Angles
An angle measures the amount of turn.

Types of angles.

Line and Line segment
In geometry a line:is straight (no bends),has no thickness, and
extends in both directions without end (infinitely).A line has no end points.

A line segment is a line having end pionts.

Complementary Angles
Two angles are said to be complementary to each other if sum of their measures is 90°.

For example, if ∠A = 50° and ∠B = 40°, then angles ∠A and ∠B are complementary to each other.

Supplementary Angles
Two angles are said to be supplementary to each other if sum of their measures is 180°.

For example, the angles whose measures are 120° and 60° are supplementary to each other.

Vertical Angles
The angles opposite each other when two lines cross. They are always equal.

Adjacent Angles
Two angles are adjacent when they have common side and common vertex and do not overlap.

Angle POR is adjacent to angle QOR
Because,
they have a common side (line OQ)
they have a common vertex (point O)

Congruent Angles
Congruent Angles have the same angle
1.They don't have to point in the same direction.
2.They don't have to be on similar sized lines.
3.Just the same angle.

∠A = ∠B

Symmetry
Symmetry defines that one shape is exactly like the other shape when it is moved, rotated, or flipped.
The imaginary line or axis along which you fold a figure to obtain the symmetrical halves is called the line of symmetry. It basically divides an object into two mirror-image halves. The line of symmetry can be vertical, horizontal or diagonal. There may be one or more lines of symmetry.

Transversal of parallel lines
A Transversal is a line that crosses at least two other lines.
In the below figure, the line l intersects p and q at two distinct points M and N. Therefore, line l is the transversal line.

When the transversal intersects two parallel lines:
• Pairs of corresponding angles are equal.
• Pairs of alternate angles are equal
• Interior angles on the same side of the transversal are supplementary.

Example 1:
How many sides does a decagon have?
Ans : 10 sides.

   Heptagon: 7 sides
   Nonagon: 9 sides
   Decagon : 10 sides
   Quadrilateral : 4 sides

Example 2:
Is this a polygon?

Ans: No

   A polygon is a closed figure with straight sides. A closed figure starts and ends at the same point.
   solve
   This figure is not a polygon. Although it is closed, it does not have straight sides.

Example 3:
Is this shape a regular polygon?

Ans: No
   A polygon is regular if all of its sides have the same length and all of its angles have the same measure.
   solve
   This shape is not a regular polygon.
   Its sides have different lengths and its angles have different measures.

Example 4:
A triangle has angle measurements of 70°, 89° and 31°. What kind of triangle is it?
Ans : Acute angle

   In an acute triangle, all three angles are less than 90°.
   In a right triangle, one angle is exactly 90°.
   In an obtuse triangle, one angle is greater than 90°.
   This triangle is an acute triangle. All 3 angles are less than 90°.

Topic Test - Mathematics- Year 5,6 Vic/NSW Selective Test

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