Maths · Topic 1: Year 10
Angles and trigonometry
Angle facts for lines, triangles, quadrilaterals and parallel lines, interior and exterior angles of polygons, Pythagoras' theorem, and using sine, cosine and tangent to find sides and angles in right-angled triangles.
Lessons
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1
Angle properties of triangles and quadrilaterals
The angle facts for lines, triangles, quadrilaterals and parallel lines - and how to use them, with reasons, to find missing angles step by step.
6 terms -
2
Interior angles of a polygon
Split any polygon into triangles from one corner and the angle sum drops out: (n − 2) × 180°. Use it to find missing angles and the angle of a regular polygon.
5 terms -
3
Exterior angles of a polygon
Walk all the way round any polygon and you turn through exactly one full turn. So the exterior angles always add up to 360° - the quickest route to the angles…
4 terms -
4
Pythagoras' theorem 1
In a right-angled triangle, the square on the longest side equals the sum of the squares on the other two. Use it to find any missing side - and to check…
4 terms -
5
Pythagoras' theorem 2
Pythagoras hidden inside other problems: the distance between two points, the height of an isosceles triangle, the slant side of a trapezium, and two triangles…
4 terms -
6
Trigonometry 1
Sine, cosine and tangent link the angles of a right-angled triangle to its sides. Label the sides, choose the right ratio, and you can find any missing side.
6 terms -
7
Trigonometry 2
Running trigonometry backwards to find a missing angle, the exact trig values you must know without a calculator, and angles of elevation and depression.
5 terms
Downloads
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- Angle properties of triangles and quadrilaterals.pptx Built from the lesson script on 29 September 2026. View
- Angle properties of triangles and quadrilaterals - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 29 September 2026. View
- Angle properties of triangles and quadrilaterals - Exam Questions.docx Built from the lesson script on 29 September 2026. View
- Interior angles of a polygon.pptx Built from the lesson script on 29 September 2026. View
- Interior angles of a polygon - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 29 September 2026. View
- Interior angles of a polygon - Exam Questions.docx Built from the lesson script on 29 September 2026. View
- Exterior angles of a polygon.pptx Built from the lesson script on 29 September 2026. View
- Exterior angles of a polygon - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 29 September 2026. View
- Exterior angles of a polygon - Exam Questions.docx Built from the lesson script on 29 September 2026. View
- Pythagoras theorem 1.pptx Built from the lesson script on 29 September 2026. View
- Pythagoras theorem 1 - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 29 September 2026. View
- Pythagoras theorem 1 - Exam Questions.docx Built from the lesson script on 29 September 2026. View
- Pythagoras theorem 2.pptx Built from the lesson script on 29 September 2026. View
- Pythagoras theorem 2 - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 29 September 2026. View
- Pythagoras theorem 2 - Exam Questions.docx Built from the lesson script on 29 September 2026. View
- Trigonometry 1.pptx Built from the lesson script on 29 September 2026. View
- Trigonometry 1 - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 29 September 2026. View
- Trigonometry 1 - Exam Questions.docx Built from the lesson script on 29 September 2026. View
- Trigonometry 2.pptx Built from the lesson script on 29 September 2026. View
- Trigonometry 2 - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 29 September 2026. View
- Trigonometry 2 - Exam Questions.docx Built from the lesson script on 29 September 2026. View
Key terms in this chapter
All 34, gathered from every lesson.
- Vertically opposite
- The angles opposite each other where two lines cross; they are equal.
- Isosceles
- A triangle with two equal sides and two equal angles.
- Parallel
- Lines that are always the same distance apart and never meet.
- Transversal
- A line that crosses two or more other lines.
- Alternate angles
- Angles on opposite sides of a transversal, between parallel lines; they are equal.
- Co-interior angles
- Angles on the same side of a transversal, between parallel lines; they add up to \(180^\circ\).
- Polygon
- A closed 2D shape with straight sides.
- Vertex
- A corner of a shape (plural: vertices).
- Interior angle
- An angle inside a polygon at a vertex.
- Regular polygon
- A polygon with all sides and all angles equal.
- Diagonal
- A straight line joining two vertices that are not next to each other.
- Exterior angle
- The angle between one side of a polygon and the extension of the side next to it.
- Interior angle
- The angle inside a polygon at a vertex.
- Angles around a point
- Angles meeting at a point; they add up to \(360^\circ\).
- Regular polygon
- A polygon with all sides and all angles equal.
- Hypotenuse
- The longest side of a right-angled triangle, opposite the right angle.
- Pythagoras' theorem
- In a right-angled triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse.
- Pythagorean triple
- Three whole numbers that fit the theorem, such as 3, 4, 5.
- Surd
- A square root that cannot be written exactly as a fraction, such as \(\sqrt{2}\).
- Hypotenuse
- The longest side of a right-angled triangle, opposite the right angle.
- Line of symmetry
- A line that splits a shape into two mirror-image halves.
- Perpendicular height
- The height measured at right angles to the base.
- Coordinates
- A pair of numbers \((x, y)\) giving the position of a point.
- Hypotenuse
- The side opposite the right angle; the longest side.
- Opposite
- The side across from the angle being used.
- Adjacent
- The side next to the angle being used, which is not the hypotenuse.
- Sine (sin)
- \(\sin\theta = \frac{\text{opp}}{\text{hyp}}\).
- Cosine (cos)
- \(\cos\theta = \frac{\text{adj}}{\text{hyp}}\).
- Tangent (tan)
- \(\tan\theta = \frac{\text{opp}}{\text{adj}}\).
- Inverse function
- \(\sin^{-1}\), \(\cos^{-1}\) or \(\tan^{-1}\): finds the angle from a ratio.
- Exact value
- A trig value written exactly, as a fraction or surd, not a rounded decimal.
- Angle of elevation
- The angle measured up from the horizontal.
- Angle of depression
- The angle measured down from the horizontal.
- Clinometer
- An instrument for measuring angles of elevation.