به انگلیسی

Shape families: rectangles, squares, and more

Mathematics · Geometry · ages 10-11

Name ______________________ Date ____________

Three rectangles have neighbouring side lengths of 3 cm and 3 cm, 6 cm and 4 cm, and 8 cm and 8 cm. How many of these rectangles are also squares?
Answer: ______________
Starting at one corner and going round a parallelogram, which side-length list is possible?
- 5 cm, 3 cm, 5 cm, 3 cm
- 5 cm, 5 cm, 3 cm, 3 cm
- 5 cm, 3 cm, 3 cm, 3 cm
- 5 cm, 3 cm, 5 cm, 4 cm
Which shape is always a rectangle?
- Any rhombus
- Any square
- Any parallelogram
What do all parallelograms have in common?
- Four corners that are all right angles
- Four sides that are all equal in length
- Two pairs of opposite parallel sides
A quadrilateral has two pairs of parallel sides, four equal sides and no right angles. How many of these names fit it: quadrilateral, parallelogram, rectangle, rhombus, square?
Answer: ______________
Which order puts each later shape family inside the family before it?
- Square, then rectangle, then parallelogram
- Rectangle, then parallelogram, then square
- Parallelogram, then rectangle, then square
A diagram puts the whole rectangle family inside the rhombus family. Which repair shows their correct relationship within parallelograms?
- Keep rectangles inside rhombuses; put squares outside both families
- Put rhombuses inside rectangles; put squares outside both families
- Overlap rectangles and rhombuses; put squares in the overlap
- Separate rectangles from rhombuses; put squares outside both families
Some parallelograms belong to neither the rectangle family nor the rhombus family.
Circle one: True False
Jun says, "This quadrilateral has four equal sides, so it must be a square." It has no right angles. What did Jun leave out?
- He assumed that a square must have unequal neighbouring sides
- He assumed that equal sides also guarantee right angles
- He checked every square rule, so his conclusion must be correct
Someone claims, "All parallelograms are regular polygons." Which shape is a counterexample?
- A square with four equal sides and four right angles
- A rectangle with sides of 9 cm, 2 cm, 9 cm and 2 cm
- A regular triangle with three equal sides and angles
- A regular hexagon with six equal sides and angles

Answer key

For grown-ups. Fold this page away before handing over the rest.

Shape families: rectangles, squares, and more W1-mt_liIW336odh-s1

2 · The 3 cm by 3 cm and 8 cm by 8 cm rectangles have four equal sides. The 6 cm by 4 cm rectangle does not. Two are squares.
5 cm, 3 cm, 5 cm, 3 cm · Opposite sides of a parallelogram match. In the 5, 3, 5, 3 list, the two 5 cm sides are opposite, and the two 3 cm sides are opposite.
Any square · Every square has four right angles and equal opposite sides, so it meets the rectangle rules.
Two pairs of opposite parallel sides · Every parallelogram has two pairs of parallel opposite sides. Four right angles and four equal sides are extra properties that not every parallelogram has.
3 · Quadrilateral, parallelogram and rhombus fit. Rectangle and square need four right angles, so they do not fit. Three listed names apply.
Parallelogram, then rectangle, then square · Every rectangle is a parallelogram, and every square is a rectangle. The path is parallelogram, rectangle, square.
Overlap rectangles and rhombuses; put squares in the overlap · Neither family contains every member of the other. Squares have both four right angles and four equal sides, so they belong in the overlap.
True · A parallelogram can have no right angles and unequal neighbouring sides. It is then neither a rectangle nor a rhombus, so those two families do not cover all parallelograms.
He assumed that equal sides also guarantee right angles · Four equal sides do not guarantee a square. A square also needs four right angles, and Jun's quadrilateral has none.
A rectangle with sides of 9 cm, 2 cm, 9 cm and 2 cm · The 9 cm by 2 cm rectangle is a parallelogram, but its unequal side lengths make it irregular. It disproves the claim.