Symmetry & Shapes Flashcards

All 22 cards in this deck

What is the mathematical name for an angle smaller than $90°$?

Acute.

What is the mathematical name for an angle greater than $90°$ but less than $180°$?

Obtuse.

What is the mathematical name for an angle greater than $180°$ but less than $360°$?

Reflex.

On a diagram, how are a right angle, a pair of parallel lines and a pair of equal sides each marked?

Right angle: a small square in the corner.
Parallel lines: matching arrowheads.
Equal sides: matching dashes.

In triangle $ABC$, which angle is meant by 'angle $ABC$'?

The angle at vertex $B$, between sides $BA$ and $BC$.

What are the mathematical names of polygons with 5, 6, 7 and 8 sides?

Pentagon (5), hexagon (6), heptagon (7), octagon (8).

True or false? Lines marked with matching arrowheads on a diagram are perpendicular.

False. Matching arrowheads mean the lines are parallel; perpendicular lines are shown with a small square.

What is a line of symmetry of a 2D shape?

A mirror line: folding the shape along it makes the two halves match exactly.

How many lines of symmetry does a regular polygon have?
e.g. a regular hexagon

The same number as its sides.
A regular hexagon has 6.

What are the steps to find all the lines of symmetry of a 2D shape?
e.g. a rectangle

1. Try each possible mirror line through the shape (through vertices or through midpoints of sides).
2. Check that folding along it makes both halves match exactly.
3. Count the lines that work: a rectangle has 2.

A shape has a line of symmetry. What does this tell you about the sides and angles on either side of that line?

Sides and angles that reflect onto each other are equal.

What are the steps to complete a shape so that a given line is a line of symmetry?
e.g. half a shape drawn to the left of a vertical mirror line

1. Measure each vertex's distance from the mirror line.
2. Mark a matching point the same distance on the other side (to the right).
3. Join the new points in the same order to complete the shape.

What does the order of rotational symmetry of a shape mean?

The number of times the shape looks exactly the same during one full turn ($360°$).

What is the order of rotational symmetry of a regular polygon?
e.g. a regular pentagon

The same as its number of sides.
A regular pentagon has order 5.

True or false? A shape with no rotational symmetry has rotational symmetry of order 0.

False. It has order 1, because every shape fits onto itself once in a full turn.

What are the steps to work out the order of rotational symmetry of a shape?
e.g. a rectangle

1. Put a pencil point (or finger) on the centre of the shape.
2. Turn the shape one full turn, counting each position where it looks the same.
3. That count is the order: a rectangle has order 2.

Through what angle must you turn a shape with rotational symmetry of order 4 for it to look the same?

$90°$, since $360 \div 4 = 90$.

Which quadrilateral should you draw for 'no lines of symmetry and rotational symmetry of order 2'?

A parallelogram that is not a rectangle or a rhombus.

What is a plane of symmetry of a 3D solid?

A flat cut that divides the solid into two identical halves, each a mirror image of the other.

How many planes of symmetry does a cube have?

How many planes of symmetry does a cuboid whose edges are all different lengths have?

3, one halfway through each pair of opposite faces.

True or false? A square-based pyramid has 4 planes of symmetry.

True. Two through the midpoints of opposite base edges and two through the base diagonals.