Download Integers 1a

Geometry 1a
Pupil Notes and worked examples
Key Skill 1: Describe various types of angles
An acute angle is an angle between 0° and 90°
A right angle is an angle of 90°
An obtuse angle is an angle between 90° and 180°
A straight angle is an angle of 180°
A reflex angle is an angle between 180° and 360°
A full turn is an angle of 360°
The equilateral triangle has 3 sides of the same length and 3 angles of the same size (60°)
The isosceles triangle has 2 sides of equal length and the 2 angles opposite these sides are
equal in size.
The scalene triangle has 3 sides of different lengths and has 3 angles of different sizes.
The right-angled triangle contains one 90° angle.
The obtuse-angled triangle contains one obtuse angle i.e. an angle larger than 90°
Equilateral
Isosceles
Right-angled
Scalene
Obtuse-angled
Key Skill 2: Naming angles
The lines TI and PI are called the arms of the angle.
The point I is called the vertex
T
The vertex must be the middle letter of its name.
You use three letters when naming angles.
I
P
All angles have 2 possible names.
The possible names of this angle are
TIP or
PIT
Information on the similarities and differences between quadrilaterals
The square has 4 right angles, 4 sides of equal length and 2 pairs of parallel lines.
The rectangle has 4 right angles, 2 pairs of sides of equal length and 2 pairs of parallel lines.
The parallelogram has 2 pairs of equal angles, 2 pairs of sides of equal length and 2 pairs of
parallel lines.
The kite has 1 pair of equal angles, 2 pairs of sides of equal length and no parallel lines.
The rhombus has 2 pairs of equal angles, 4 sides of equal length and no parallel lines.
The trapezium has 1 pair of parallel lines.
Square
Trapezium
Rectangle
Rhombus
Parallelogram
Kite
Key Skill 3: Accurately draw triangles and basic quadrilaterals
Using a ruler, protractor and a pair of compasses you can draw triangles and quadrilaterals.
Let’s draw this
Triangle
45°

5 cm
75°
Draw your base
5 cm
 Measure your
45° angle
Measure your
75° angle
 Rub out the lines outwith your triangle to finish
(Remember to label your angles and sides)
45°
5 cm
75°
Key Skill 4: Use several methods to accurately draw triangles
Method 1: Draw a triangle given the length of the base and 2 angles (as above)
Method 2: Draw a triangle given the lengths of all 3 sides (as below)
Let’s draw this
Triangle
Draw your base 
4 cm
4.5 cm
6 cm
6 cm
Set your pair of compasses 4 cm apart
and draw an arc from the left hand side
of the base
Set your pair of compasses 4.5 cm apart
and draw an arc from the right hand side
of the base
The point where the 2 arcs meet should join
the 2 ends of the base to complete your triangle
Finally, remember to label your sides
4 cm
4.5 cm
6 cm
Key Skill 5: Calculate the unknown angles within any triangle
You should be able to find any unknown angles by remembering the triangle properties above and
knowing that all three angles in a triangle add up to 180°.
To calculate the missing angle 83° + 38° = 121°
e.g.
83°
180° - 121° = 59°
38°
Key Skill 6: Calculate the unknown angles within any quadrilateral
You should be able to find any unknown angles by remembering the quadrilateral properties
above and knowing that all four angles in a quadrilateral add to 360°
e.g.
78°
61°
To calculate the missing angle 119° + 61°+ 78° = 258°
360° - 258° = 102°
119°
Key Skill 7: Find the perimeter of triangles and quadrilaterals in mm and cm
The perimeter of a shape is the distance around it.
This can be found by adding each of the sides lengths.
e.g.
Perimeter (P) = 18 + 18 + 16
18 cm
18 cm
P = 52 cm
16 cm
1 cm = 10 mm
7.5 cm
7.5 cm = 75 mm
18 mm
18 mm
Perimeter (P) = 75 + 18 + 18 + 29
P = 140 mm
2.9 cm
2.9 cm = 29 mm