Angles, Triangles and Polygons

Key Concepts:
Angle: A measure of rotation between two lines that meet at a point.
Polygon: A closed 2D shape made from straight lines only (sides do NOT have to be equal length). The lines must not cross each other.
Regular Polygon: A special polygon where ALL sides are equal length AND ALL angles are equal.
Quadrilateral: Any polygon with exactly 4 sides.

Section A: Drawing Basic Angles

1 Draw the following angles in the boxes provided [3]

Instructions: Use your protractor to draw each angle accurately. Label each angle clearly.

a) An acute angle

(Any angle less than 90°)

b) An obtuse angle

(Any angle between 90° and 180°)

c) An angle of 56°

(Use your protractor!)

2 Draw these specific angles using your protractor [4]

a) 35°

b) 125°

c) 90° (right angle)

d) 160°

Section B: Drawing Combinations of Lines and Angles

3 Draw the following combinations of lines and angles [5]

a) Draw three lines that meet at a point, forming two acute angles

Hint: Start with a point, then draw three lines from it. Check that two of the angles formed are acute (less than 90°).

b) Draw four lines that meet at a point, with one right angle and two obtuse angles

Hint: Use your protractor to ensure accuracy.

c) Draw two intersecting lines forming angles of 45° and 135°

Hint: When two straight lines cross, they create two pairs of equal angles.

Section C: Types of Triangles

4 Draw these triangles based on the given descriptions [5]

Tip: Try drawing more than one example of each triangle type in the box to show different variations!

a) An equilateral triangle

All sides equal, all angles 60°

b) An isosceles triangle

Two sides equal, two angles equal

c) A right-angled triangle

One angle = 90°

d) A scalene triangle

All sides different lengths

e) A right-angled isosceles triangle

One 90° angle, two equal sides

Section D: Understanding and Drawing Polygons

What is a Polygon?
A polygon is a closed 2D shape made entirely from straight lines. The lines must connect to form a complete shape with no gaps. The lines must NOT cross each other. The sides do NOT have to be the same length (unless it's a regular polygon).

5 Which of these are polygons? Write YES or NO [5]

a) A triangle ___________

b) A circle ___________

c) A square ___________

d) A shape with one curved side and three straight sides ___________

e) A pentagon (5-sided shape) ___________

6 Draw these polygons in the boxes [6]

Remember: Polygons are closed shapes made only from straight lines. The sides don't have to be the same length. Use a ruler!

a) A triangle (3 sides)

b) A quadrilateral (4 sides)

c) A pentagon (5 sides)

d) A hexagon (6 sides)

e) A heptagon (7 sides)

f) An octagon (8 sides)

Section E: Regular Polygons

7 Draw these regular polygons as accurately as you can [4]

a) An equilateral triangle

(All sides equal, all angles 60°)

b) A square

(All sides equal, all angles 90°)

c) A regular pentagon

(5 equal sides, 5 equal angles)

d) A regular hexagon

(6 equal sides, 6 equal angles)

Section F: Special Quadrilaterals

8 Draw a few examples of each special quadrilateral [12]

Use a ruler and pay attention to the specific properties of each shape!

a) Squares

All sides equal, all angles 90°

b) Rectangles (not squares)

Opposite sides equal, all angles 90°

c) Rhombuses

All sides equal, opposite angles equal

d) Parallelograms (not rectangles)

Opposite sides parallel and equal

e) Kites

Two pairs of adjacent equal sides

f) Trapeziums

One pair of parallel sides

Section G: Combining Polygons and Angles

9 Draw shapes with specific angle requirements [6]

a) Draw a quadrilateral with two right angles and two acute angles

Label all angles clearly.

b) Draw a pentagon where three angles are 90° and mark them

Use the right angle symbol to mark the 90° angles.

c) Draw an octagon with at least four right angles

Remember: An octagon has 8 sides.

10 Create composite shapes (combining polygons) [6]

a) Draw a shape made by joining two equilateral triangles together along one side

What is this shape called?

Name: _______________________________________________

b) Draw a hexagon by combining a square and two equilateral triangles

Place one triangle on top of the square and one on the bottom.

c) Draw a pattern using at least 3 regular polygons of your choice

Be creative! The polygons can be the same or different types.