Geometry: Angles, Shapes and Reflection
Geometry: Angles, Shapes and Reflection is the Year 5 topic covering classifying and estimating acute, obtuse and reflex angles, using the facts that angles on a straight line add up to 180 degrees and angles around a point add up to 360 degrees, and reflecting a 2D shape in a mirror line on a coordinate grid.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the four angle types by their size: acute (less than 90 degrees), right angle (exactly 90 degrees), obtuse (between 90 and 180 degrees) and reflex (between 180 and 360 degrees).
- To estimate an angle before measuring, compare it to a right angle (a square corner): is it smaller, close to it, bigger but less than a straight line, or bigger than a straight line?
- Remember that angles on a straight line always add up to 180 degrees, so a missing angle on a straight line is 180 minus the angle(s) you already know.
- Remember that angles around a full point always add up to 360 degrees, so a missing angle around a point is 360 minus the angle(s) you already know.
- To reflect a shape in a vertical or horizontal mirror line, reflect one vertex at a time: count its distance from the mirror line, then mark the image the same distance on the other side.
- Check a reflection is correct by confirming the shape and size have not changed, only the position, and that each point and its image are the same distance from the mirror line.
- When a mirror line is given as a line on a coordinate grid (e.g. the line x = 5), reflect each vertex's coordinate individually before joining them up.
Worked example
Triangle ABC has vertices at A(1,1), B(1,4) and C(3,1) on a coordinate grid. Reflect the triangle in the vertical mirror line x = 5, and give the coordinates of the reflected triangle.
- Find each vertex's horizontal distance from the mirror line x = 5: A(1,1) is 5 - 1 = 4 units away, B(1,4) is also 4 units away, and C(3,1) is 5 - 3 = 2 units away.
- Reflect each vertex the same distance on the other side of the line x = 5, keeping the y-coordinate the same: A(1,1) maps to (5 + 4, 1) = (9,1).
- B(1,4) maps to (5 + 4, 4) = (9,4).
- C(3,1) maps to (5 + 2, 1) = (7,1).
- So the reflected triangle A'B'C' has vertices at (9,1), (9,4) and (7,1).
Practice questions
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Q1Classify this angle: it measures 35 degrees. Is it acute, right, obtuse or reflex?Show answer
Answer: Acute (it is less than 90 degrees).
Q2Classify this angle: it measures 210 degrees. Is it acute, right, obtuse or reflex?Show answer
Answer: Reflex (it is between 180 and 360 degrees).
Q3Two angles on a straight line are 68 degrees and an unknown angle. Find the missing angle.Show answer
Answer: 112 degrees (180 - 68 = 112)
Q4Three angles meet at a point. Two of them measure 95 degrees and 140 degrees. Find the third angle.Show answer
Answer: 125 degrees (360 - 95 - 140 = 125)
Q5A point P is plotted at (2,3). Reflect P in the horizontal mirror line y = 1. What are the coordinates of the image?Show answer
Answer: (2,-1), since P is 2 units above the line (3 - 1 = 2), so its image is 2 units below the line (1 - 2 = -1).
Q6A shape is reflected in a mirror line. Does the reflected shape change size?Show answer
Answer: No, reflection changes only the position of a shape, never its size or shape.
Q7A rectangular window frame has a diagonal support bar from one corner. The bar splits the 90-degree corner into two angles, one of which measures 38 degrees. Find the size of the other angle.Show answer
Answer: 52 degrees (90 - 38 = 52)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A straight line is split into three angles by two rays. The first angle measures 47 degrees and the second measures 82 degrees. Find the third angle, and state whether it is acute, obtuse or reflex.
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Rectangle PQRS has vertices at P(2,2), Q(2,5), R(6,5) and S(6,2) on a coordinate grid. The rectangle is reflected in the vertical mirror line x = 8. (a) Give the coordinates of P after the reflection. (2 marks) (b) State one property of the rectangle that stays the same after the reflection. (1 mark)
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An angle measures 265 degrees. Is this angle acute, obtuse or reflex?
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Free printable worksheet
Want more practice on paper? Download the geometry: angles, shapes and reflection worksheet pack - 5 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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