Year 10 / GCSE · Maths
Shapes And Geometry
Year 10 / GCSE learners practise circle theorems and transformations gcse.
The activities include Apply Alternate Segment Theorem, Apply Chords and Radii, Apply Circle Theorems to Solve Problems, and related practice. The checked support below includes video, teaching, worksheet, practice. Open a resource in its provider's website and choose the format that best helps the learner explain the idea independently.
Activities covered
- Apply Alternate Segment Theorem
- Apply Chords and Radii
- Apply Circle Theorems to Solve Problems
- Apply Cyclic Quadrilateral Theorem
- Apply Exact Trig Values
- Apply Ratios to Map Scales
- Apply Tangents to a Circle
- Apply the Angles Around the Centre of a Circle Rule
- Apply the Angles in the Same Segment Rule
- Apply the Properties of Quadrilaterals
- Apply Theorem relating to Angles Subtended from the Diameter
- Apply Trigonometry Knowledge to 3D Shapes
- Describe All Transformations
- Describe Congruent Transformations
- Draw Plans and Elevations of 3D Shapes
- Enlarge 2D Shapes
- Enlarge from a Given Point
- Enlarge Using a Fractional Scale Factor
- Enlarge Using a Negative Scale Factor
- Find a Missing Angle Using the Cos Ratio
- Find a Missing Angle Using the Sin Rule
- Find a Missing Angle Using the Tan Ratio
- Find a Missing Side Using the Cos Ratio
- Find a Missing Side Using the Sin Ratio
- Find a Missing Side Using the Tan Ratio
- Find a Side Using the Cosine Rule
- Find an Angle Using the Cosine Rule
- Find an Angle Using the Sin Ratio
- Find Angles Using Knowledge of Sectors
- Find Compound Perimeters
- Find the Area of a Sector
- Find the Area of Compound Shapes
- Find the Area of Similar Shapes
- Find the Hypotenuse Using Pythagoras' Theorem
- Find the Length of an Arc
- Find the Surface Area of a Pyramid
- Find the Surface area of a Pyramid
- Find the Volume of a Pyramid
- Find the Volume of Frustums
- Finding the Shorter Side Using Pythagoras' Theorem
- Identify 3D Shapes
- Identify Faces, Edges and Vertices of 3D Shapes
- Identify Invariant Points
- Identify Reflective Symmetry
- Identify Similar Shapes
- Identify the Properties of a Circle
- Interpret Plans and Elevations
- Label Sides of a Triangle
- Leave Answers in Terms of Pi
- Recall 2D Geometry Notation and Terms
- Recall 3D Geometry Notation and Terms
- Recognise Rotational Symmetry
- Rotate a Shape
- Solve Complex problems Using Pythagoras' Theorem
- Solve Loci Problems
- Solve Problems Using Pythagoras' Theorem
- Solve Trigonometry Problems
- Translate an Object
- Understand and Read Bearings
- Understand Conversion in Scale Drawings
- Using Pythagoras' Theorem on 3D Shapes
Checked learning resources
-
The alternate segment theorem
Oak National Academy · Video · Opens on the provider website
Year 10 Higher Maths lesson deriving and applying the alternate segment theorem: the angle between a tangent and a chord equals the angle in the alternate segment, with unknown-angle and multi-step circle problems.
-
A perpendicular radius bisects a chord
Oak National Academy · Video · Opens on the provider website
Year 10 Higher Maths lesson deriving and applying the fact that a perpendicular from the centre of a circle to a chord bisects that chord, using the right angle and equal half-chords to calculate missing angles and side
-
Problem solving with circle theorems
Oak National Academy · Video · Opens on the provider website
Year 10 Higher Maths lesson selecting and combining circle theorems to solve multi-step geometric problems, including equal angles subtended by the same chord and adding construction lines where needed.
-
Opposite angles in a cyclic quadrilateral sum to 180 degrees
Oak National Academy · Video · Opens on the provider website
Year 10 Higher Maths lesson deriving and applying the cyclic quadrilateral theorem to calculate unknown angles and solve linked angle problems where all four vertices lie on a circle.
-
Exact trigonometric values for 30 and 60 degrees
Oak National Academy · Video · Opens on the provider website
Year 10 Higher Maths lesson deriving and calculating the exact sine, cosine and tangent values for 30° and 60° from special triangles, leaving answers in exact surd or fractional form.
-
Real-world ratios and map scales
Oak National Academy · Video · Opens on the provider website
GCSE Maths lesson interpreting map scales such as 1 : 250,000 as a ratio, keeping both quantities in the same units, and converting between a measured map distance and the corresponding real-life distance.
-
A tangent is perpendicular to the radius at the point of contact
Oak National Academy · Video · Opens on the provider website
Year 10 Higher Maths lesson deriving and applying the theorem that a tangent touching a circle is perpendicular to the radius at the point of contact, using the resulting right angle to find unknown angles and lengths.
-
The angle at the centre is twice the angle at the circumference
Oak National Academy · Video · Opens on the provider website
Year 10 Higher Maths lesson deriving and applying the theorem that an angle subtended at the centre is twice the angle subtended by the same arc at the circumference, including doubling, halving and linked angle reasonin