Triangles
Types of triangle
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A triangle is a Having only two dimensions, usually length (or height) and width. shape with three sides. There are four different triangles with different properties.
A scalene triangle has 3 sides of different lengths and 3 unequal angles.
An isosceles triangle has 2 sides of equal length. The dashes on the lines show they are equal in length. The angles at the base of the equal sides are equal.
An equilateral triangle has 3 sides of equal length. The dashes on the lines show they are equal in length. All of the angles are also equal.
A right-angled triangle is a triangle that has a right angle.
Labelling angles and sides
Letters can be used to label angles.
AB and AC are A line segment is part of a line which has two end points (ie, it is not infinite)., and they meet at point A. AB joins the points A and B.
The angle between AB and AC is labelled BAC.
The angle can written as BAC or BÂC or ∠BAC.
Interior and exterior angles
The angles inside a shape are called interior angles.
If the side of a triangle is extended, the angle formed outside the triangle is the exterior angle.
\(g\) is the interior angle. \(h\) is the exterior angle. \(g + h = 180^\circ\)
The interior angle and its corresponding exterior angle always add up to 180°.
The sum of interior angles in a triangle
To prove \(a + b + c = 180^\circ\), firstly draw a line parallel to one side of the triangle.
\(d = b\) (alternate angles are equal)
\(e = c\) (alternate angles are equal)
\(a + d + e = 180^\circ\) (angles on a straight line add up to 180°)
So \(a + b + c = 180^\circ\).
These facts can be used to calculate angles.
Question
Calculate the angles \(m\) and \(n\).
\(m = 180^\circ - 90^\circ - 50^\circ = 40^\circ\)
\(n = 180^\circ - 50^\circ = 130^\circ\)
More guides on this topic
- NEW: Angles
- NEW: Angles in parallel lines
- NEW: Polygons
- NEW: Line and rotational symmetry
- NEW: Constructing triangles
- NEW: Ruler and compass constructions
- NEW: Loci
- NEW: Bearings
- NEW: Perimeter
- NEW: Area
- NEW: Volume of a prism
- NEW: Surface area of a prism
- NEW: Pyramids, cones and spheres
- NEW: Nets, plans and elevations
- NEW: Circumference and arc length
- NEW: Area of circles and sectors
- NEW: Higher – Circle Theorems – Calculating angles using circles
- NEW: Higher – Using the alternate segment theorem, tangents and chords
- NEW: Reflection
- NEW: Rotation
- NEW: Translation
- NEW: Enlargement
- NEW: Higher − Negative enlargements
- NEW: Higher – Combined transformations and invariant points
- NEW: Congruent and similar shapes
- NEW: Higher – Similarity in 2D and 3D shapes
- NEW: Pythagoras' theorem
- NEW: Solving 2D and 3D problems using Pythagoras' theorem
- NEW: Right-angled trigonometry
- NEW: Exact trigonometric values
- NEW: Higher – Sine rule
- NEW: Higher – Cosine rule
- NEW: Higher – 2D and 3D trigonometry problems
- NEW: Vectors
- NEW: Higher – Geometric problems using vectors
- Loci and constructions - AQA
- 2-dimensional shapes - AQA
- 3-dimensional shapes - AQA
- Circles, sectors and arcs - AQA
- Circle theorems - Higher - AQA
- Transformations - AQA
- Pythagoras' theorem - AQA
- Units of measure - AQA
- Trigonometry - AQA
- Vectors - AQA
