Notation and drawing Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Notation and drawing questions. See exactly how to solve problems on three-letter angle notation, vertex, polygon names, counting sides.

three-letter angle notationvertexpolygon namescounting sidestriangle typesequilateral
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
The angle ABC\angle ABC is marked in a diagram. Which letter names the vertex of this angle?

Worked solution

  1. Read the three letters in order

    ABC\angle ABC

    The three letters are A, then B, then C.

  2. Recall the rule for three-letter angle notation

    ABC    vertex=B\angle ABC \;\rightarrow\; \text{vertex} = B

    In three-letter angle notation the MIDDLE letter is always the vertex, the corner where the two arms meet.

  3. Name the vertex

    B

    The middle letter is B, so the angle is at B, between the arms BA and BC.

Answer
B\text{B}
Question 2
1 markeasy
How many sides does a pentagon have?

Worked solution

  1. Recall the polygon names

    penta-=5\text{penta-} = 5

    The prefix "penta" means five.

  2. Apply it to the polygon

    pentagon5 sides\text{pentagon} \rightarrow 5 \text{ sides}

    A pentagon is a polygon with five straight sides.

  3. State the answer

    55

    A pentagon has 5 sides.

Answer
55
Question 3
1 markeasy
A triangle has three sides that are all 7 cm long. Give the mathematical name of this triangle.

Worked solution

  1. Compare the three sides

    7=7=77 = 7 = 7

    All three sides are the same length.

  2. Recall the triangle names

    3 equal sidesequilateral\text{3 equal sides} \rightarrow \text{equilateral}

    A triangle with three equal sides is equilateral; its three angles are all 60 degrees.

  3. State the answer

    Equilateral triangle\text{Equilateral triangle}

    So it is an equilateral triangle.

Answer
Equilateral triangle\text{Equilateral triangle}
Question 4
1 markeasy
How many lines of symmetry does a square have?

Worked solution

  1. Look for the two mirror lines through the midpoints of the sides

    vertical+horizontal=2\text{vertical} + \text{horizontal} = 2

    One mirror line runs across the middle from top to bottom, one from side to side.

  2. Look for the two mirror lines along the diagonals

    two diagonals=2\text{two diagonals} = 2

    Each diagonal of a square is also a mirror line.

  3. Add them up

    2+2=42 + 2 = 4

    A square has 4 lines of symmetry in total.

Answer
44
Question 5
1 markeasy
Two straight lines in the same plane never meet, however far they are extended. Which word describes these two lines?

Worked solution

  1. Picture the two lines

    never meet\text{never meet}

    The lines keep the same distance apart forever.

  2. Recall the word

    ABCDAB \parallel CD

    Lines that never meet are parallel. Parallel lines are marked with matching arrows and written with the symbol \parallel.

  3. State the answer

    Parallel\text{Parallel}

    The word is "parallel".

Answer
Parallel\text{Parallel}

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