Triangles Flashcards
What is a triangle?
A triangle is any three sided 2D shape.
How can triangles be classified?
According to the length of their sides and according to the size of their angles.
How can triangles be classified according to their sides?
Equilateral triangles
Isosceles triangles
Scalene triangles
How can triangles be classified according to the size of their angles?
Right angled triangles
Obtuse angled triangles
Acute angled triangles
What are the properties of isosceles triangles?
They have two adjacent sides that are equal in length
The angles opposite the sides of equal length are equal
What are the properties of a scalene triangle?
They have no sides of equal length
They have no equal angles
What are the properties of right angled triangles?
They have one angle that is equal to 90°
A right angled triangle can also be a scalene or isosceles triangle
What are the properties of an obtuse angled triangle?
It has one obtuse angle
An obtuse angled triangle can also be an isosceles triangle
What are the properties of an acute angled triangle?
It has three acute angles
An acute angled triangle can also be an equilateral triangle
What are the properties of equilateral triangles?
They have three sides of equal length
They have three equal angles
Each of the angles is 60°
In a triangle, which side is the longest side?
The longest side is always opposite the largest angle.
What are the properties of triangles?
They have three sides
They have three angles
If one of the sides of a triangle is produced (extended) then the new angle created on the outside of the triangle is equal to the sum of the two opposite interior angles of the triangle. We call this exterior angles of triangles.
All the angles inside a triangle add up to 180°
Where is the perpendicular height found in a right angled triangle?
The perpendicular height is found as a part of the triangle.
Where is the perpendicular height found in an acute angled triangle?
It is found inside the triangle.
Where is the perpendicular height found in an obtuse angled triangle?
The perpendicular height is found outside of the triangle.
What is the Pythagoras theorem?
The theorem states that the hypotenuse squared is equal to the sum of the other two sides squared.
What is the hypotenuse?
The hypotenuse is the side opposite the 90° angle.
It is always the longest side.
How do we use Pythagoras to work out the base of a right angled triangle?
The hypotenuse squared minus the height squared.
How do we use Pythagoras to work out the height of a right angled triangle?
The hypotenuse squared minus the base squared.
What are the Pythagoras triplets?
3;4;5
5;12;13
8;15;17
7;24;25
What are surds?
Surds are numbers that are left in square root form.
How do we simplify surds?
To simplify surds, make the number that is being square rooted a product of its prime factors. Any numbers that are repeated, place their exponential power outside the square root. Any numbers that are not repeated i.e. Not being squared, place inside the square root. If there is more than one number, multiply them together.
