Explore · MATH-5B-C11-L06-OPEN
Name a quadrilateral that can have four equal sides and four right angles with all four sides 5 cm.
Great Inheritance Mathematics Term B · Original independent course
Classifying Quadrilaterals
Watch for: Thinking a square is not also a rectangle.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C11-L06-PREREQ
How many sides does a quadrilateral have?
Show worked answer (after attempting)
Answer: 4
A quadrilateral is a four-sided polygon.
Understand the idea
Classify quadrilaterals by parallel sides, equal sides and right angles, including hierarchical families. The essential earlier idea is: 4B rectangles, squares and right angles.. The model below will always use the actual quantities from the worked problem. Check thinking a square is not also a rectangle when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C11-L06-Q01
Name a quadrilateral that can have four right angles with adjacent sides 4 cm and 6 cm.
Solution: rectangle
A quadrilateral is any simple polygon with four straight sides. A rectangle satisfies four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
Worked example 2 · MATH-5B-C11-L06-Q02
A sketch has four equal sides and four right angles and all four sides 4 cm. Name a valid quadrilateral family.
Solution: square
A quadrilateral is any simple polygon with four straight sides. A square satisfies four equal sides and four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
Worked example 3 · MATH-5B-C11-L06-Q03
Identify a quadrilateral family satisfying two pairs of parallel opposite sides and adjacent sides 4 cm and 6 cm; justify why it has four sides.
Solution: parallelogram; a quadrilateral has four sides
A quadrilateral is any simple polygon with four straight sides. A parallelogram satisfies two pairs of parallel opposite sides. Properties can overlap; a square has rectangle and parallelogram properties.
Check understanding
1 · MATH-5B-C11-L06-Q04
Name a quadrilateral that can have four equal sides and four right angles with all four sides 5 cm.
Show worked answer (after attempting)
Answer: square
A quadrilateral is any simple polygon with four straight sides. A square satisfies four equal sides and four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
2 · MATH-5B-C11-L06-Q05
A sketch has two pairs of parallel opposite sides and adjacent sides 5 cm and 7 cm. Name a valid quadrilateral family.
Show worked answer (after attempting)
Answer: parallelogram
A quadrilateral is any simple polygon with four straight sides. A parallelogram satisfies two pairs of parallel opposite sides. Properties can overlap; a square has rectangle and parallelogram properties.
3 · MATH-5B-C11-L06-Q06
Identify a quadrilateral family satisfying four right angles and adjacent sides 5 cm and 7 cm; justify why it has four sides.
Show worked answer (after attempting)
Answer: rectangle; a quadrilateral has four sides
A quadrilateral is any simple polygon with four straight sides. A rectangle satisfies four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
Guided practice
1 · MATH-5B-C11-L06-Q07
Name a quadrilateral that can have two pairs of parallel opposite sides with adjacent sides 6 cm and 8 cm.
Show worked answer (after attempting)
Answer: parallelogram
A quadrilateral is any simple polygon with four straight sides. A parallelogram satisfies two pairs of parallel opposite sides. Properties can overlap; a square has rectangle and parallelogram properties.
2 · MATH-5B-C11-L06-Q08
A sketch has four right angles and adjacent sides 6 cm and 8 cm. Name a valid quadrilateral family.
Show worked answer (after attempting)
Answer: rectangle
A quadrilateral is any simple polygon with four straight sides. A rectangle satisfies four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
3 · MATH-5B-C11-L06-Q09
Identify a quadrilateral family satisfying four equal sides and four right angles and all four sides 6 cm; justify why it has four sides.
Show worked answer (after attempting)
Answer: square; a quadrilateral has four sides
A quadrilateral is any simple polygon with four straight sides. A square satisfies four equal sides and four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
4 · MATH-5B-C11-L06-Q10
Name a quadrilateral that can have four right angles with adjacent sides 7 cm and 9 cm.
Show worked answer (after attempting)
Answer: rectangle
A quadrilateral is any simple polygon with four straight sides. A rectangle satisfies four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
Independent practice
1 · MATH-5B-C11-L06-Q11
A sketch has four equal sides and four right angles and all four sides 7 cm. Name a valid quadrilateral family.
Show worked answer (after attempting)
Answer: square
A quadrilateral is any simple polygon with four straight sides. A square satisfies four equal sides and four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
2 · MATH-5B-C11-L06-Q12
Identify a quadrilateral family satisfying two pairs of parallel opposite sides and adjacent sides 7 cm and 9 cm; justify why it has four sides.
Show worked answer (after attempting)
Answer: parallelogram; a quadrilateral has four sides
A quadrilateral is any simple polygon with four straight sides. A parallelogram satisfies two pairs of parallel opposite sides. Properties can overlap; a square has rectangle and parallelogram properties.
3 · MATH-5B-C11-L06-Q13
Name a quadrilateral that can have four equal sides and four right angles with all four sides 8 cm.
Show worked answer (after attempting)
Answer: square
A quadrilateral is any simple polygon with four straight sides. A square satisfies four equal sides and four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
4 · MATH-5B-C11-L06-Q14
A sketch has two pairs of parallel opposite sides and adjacent sides 8 cm and 10 cm. Name a valid quadrilateral family.
Show worked answer (after attempting)
Answer: parallelogram
A quadrilateral is any simple polygon with four straight sides. A parallelogram satisfies two pairs of parallel opposite sides. Properties can overlap; a square has rectangle and parallelogram properties.
5 · MATH-5B-C11-L06-Q15
Identify a quadrilateral family satisfying four right angles and adjacent sides 8 cm and 10 cm; justify why it has four sides.
Show worked answer (after attempting)
Answer: rectangle; a quadrilateral has four sides
A quadrilateral is any simple polygon with four straight sides. A rectangle satisfies four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
6 · MATH-5B-C11-L06-Q16
Name a quadrilateral that can have two pairs of parallel opposite sides with adjacent sides 9 cm and 11 cm.
Show worked answer (after attempting)
Answer: parallelogram
A quadrilateral is any simple polygon with four straight sides. A parallelogram satisfies two pairs of parallel opposite sides. Properties can overlap; a square has rectangle and parallelogram properties.
7 · MATH-5B-C11-L06-Q17
A sketch has four right angles and adjacent sides 9 cm and 11 cm. Name a valid quadrilateral family.
Show worked answer (after attempting)
Answer: rectangle
A quadrilateral is any simple polygon with four straight sides. A rectangle satisfies four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
8 · MATH-5B-C11-L06-Q18
Identify a quadrilateral family satisfying four equal sides and four right angles and all four sides 9 cm; justify why it has four sides.
Show worked answer (after attempting)
Answer: square; a quadrilateral has four sides
A quadrilateral is any simple polygon with four straight sides. A square satisfies four equal sides and four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
Challenge and error analysis
1 · MATH-5B-C11-L06-ERR1
The assigned question is: “A sketch has four right angles and adjacent sides 12 cm and 14 cm. Name a valid quadrilateral family.” A learner wrote: “I decided the quadrilateral family from only one property and labelled it square.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: rectangle
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: rectangle. Recompute from the given data: A quadrilateral is any simple polygon with four straight sides. A rectangle satisfies four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
2 · MATH-5B-C11-L06-ERR2
The assigned question is: “Identify a quadrilateral family satisfying four equal sides and four right angles and all four sides 12 cm; justify why it has four sides.” A learner wrote: “I decided the quadrilateral family from only one property and labelled it It cannot be determined from this information..” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: square; a quadrilateral has four sides
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: square; a quadrilateral has four sides. Recompute from the given data: A quadrilateral is any simple polygon with four straight sides. A square satisfies four equal sides and four right angles. Properties can overlap; a square has rectangle and parallelogram properties.
Exit check
Exit · MATH-5B-C11-L06-Q19
Name a quadrilateral that can have four right angles with adjacent sides 10 cm and 12 cm.
Show worked answer (after attempting)
Answer: rectangle
A quadrilateral is any simple polygon with four straight sides. A rectangle satisfies four right angles. Properties can overlap; a square has rectangle and parallelogram properties.