Shape Detectives
How many sides does a hexagon have?
6
What is the name of an angle that measures exactly 90°?
A right angle.
What is another name for a reflection in geometry?
A flip.
What is another name for a translation in geometry?
A slide.
What is another name for a rotation in geometry?
A turn.
What do you call a quadrilateral with two pairs of parallel opposite sides?
A parallelogram.
What type of angle measures 125°: acute, right or obtuse?
Obtuse.
When a shape is reflected, does its size change?
No. A reflection preserves its size and shape.
A shape moves 4 squares to the right without turning or flipping. Which transformation has occurred?
Translation.
How many degrees are in a half-turn?
180°.
Name a quadrilateral with exactly one pair of parallel sides.
A trapezium
Three angles in a quadrilateral are 90°, 80° and 110°. Calculate the fourth angle.
80°, because the interior angles of a quadrilateral add to 360°.
A point is 3 squares to the left of a vertical mirror line. Where will its reflection be?
3 squares to the right of the mirror line.
A point at (1, 2) is translated 3 units right and 4 units up. What are its new coordinates?
(4, 6).
A shape is rotated 90° clockwise about a fixed point. Does its size change? What happens to its orientation?
Its size does not change. Its orientation changes because it turns 90° clockwise.
A quadrilateral has four equal sides, but its angles are not all 90°. What shape is it?
A rhombus.
A triangle has angles of 45° and 65°. Find the third angle and explain your calculation.
70°. The interior angles of a triangle add to 180°, so 180° − 45° − 65° = 70°.
A triangle is reflected across a horizontal mirror line. One vertex is 2 squares above the line. Where will the corresponding vertex be?
2 squares below the line, directly opposite the original vertex.
A rectangle is translated 5 squares left and 2 squares down. What happens to its side lengths, angles and orientation?
Its side lengths and angles stay the same, and its orientation does not change. Only its position changes.
A point at (3, 1) is rotated 90° anticlockwise about the origin. What are its new coordinates?
(−1, 3). A 90° anticlockwise rotation maps (x, y) to (−y, x).
A shape has four equal sides and four right angles. Name the shape and explain why it also belongs to the family of rectangles and parallelograms.
A square. It is a rectangle because it has four right angles, and a parallelogram because both pairs of opposite sides are parallel.
A regular polygon has an exterior angle of 45°. How many sides does it have? Explain how you know.
8 sides. The exterior angles of a convex polygon add to 360°, and 360° ÷ 45° = 8.
A point is at (2, 3) on a coordinate grid. It is reflected across the y-axis. What are its new coordinates? Explain what changes.
(−2, 3). The x-coordinate changes sign, while the y-coordinate stays the same.
Triangle ABC has vertices A(1, 1), B(4, 1) and C(2, 3). It is translated 2 units left and 3 units up. Find the new coordinates of A, B and C.
A′(−1, 4), B′(2, 4), C′(0, 6).
A shape is reflected, then translated, then rotated. After all three transformations, what can you say about its size, side lengths and angles? Explain.
They remain unchanged. Reflection, translation and rotation are rigid transformations, so the final shape is congruent to the original.