This grade 5 classifying worksheet answer key solves all 24 problems of the classifying two-dimensional figures worksheet step by step.
This answer key explains each of the 24 classification problems. Check which attribute decides each name, such as parallel sides, equal sides, or right angles, and review the hierarchy whenever a true-or-false answer surprises you.
Grade 5 Classifying Worksheet Answer Key: problems 1–5
Problem 1: Triangle by sides A
Exactly two sides are equal (5 and 5), and the third is different.
Isosceles
Problem 2: Triangle by sides B
All three sides are equal, so it is equilateral. An isosceles triangle needs at least two equal sides, so it is also isosceles.
Equilateral; yes, it is also isosceles.
Problem 3: Triangle by sides C
No two sides are equal.
Scalene
Problem 4: Triangle by angles A
One angle is exactly \(90^{\circ}\).
Right triangle
Problem 5: Triangle by angles B
One angle, \(100^{\circ}\), is greater than \(90^{\circ}\), so the triangle is obtuse. Two angles are equal, which means two sides are equal.
Obtuse and isosceles
Grade 5 Classifying Worksheet Answer Key: problems 6–10
Problem 6: Triangle by angles C
All three angles are less than \(90^{\circ}\).
Acute triangle
Problem 7: Classify both ways
The sides are 3 ft, 4 ft, and 5 ft, so no two are equal. The square corner shows a \(90^{\circ}\) angle.
Scalene and right
Problem 8: Parallelogram facts
The arrows show 2 pairs of parallel sides, so P is a parallelogram.
Opposite sides of a parallelogram are equal: bottom = 8 cm, left = 5 cm.
Perimeter: \(8 + 5 + 8 + 5 = 26\) cm.
2 pairs; parallelogram; bottom 8 cm, left 5 cm; perimeter 26 cm.
Problem 9: Square or not
Four right angles make it a rectangle, and four equal sides make it a rhombus. Both together make a square.
Square
Problem 10: Rectangle riddle
Both pairs of opposite sides are parallel, so it is a parallelogram. Four right angles make it a rectangle. The sides are not all equal, so it is not a square.
Rectangle
Grade 5 Classifying Worksheet Answer Key: problems 11–15
Problem 11: One pair of parallel sides
A quadrilateral with a pair of parallel sides is a trapezoid.
The left and right sides are not parallel, so Q does not have two pairs of parallel sides. It is not a parallelogram.
Trapezoid; not a parallelogram.
Problem 12: Name the leaning shape
Opposite sides are parallel, so R is a parallelogram. All four sides are equal, so it is a rhombus.
A square must have four right angles, and R has none.
Rhombus
Problem 13: Squares and rectangles
A rectangle is a parallelogram with four right angles. Every square has four right angles and opposite sides parallel.
True
Problem 14: Rectangles and squares
A square needs four equal sides. A rectangle that is 6 inches long and 2 inches wide has four right angles but unequal sides.
False; a 6 in by 2 in rectangle is not a square.
Problem 15: Rhombus and parallelogram
A rhombus has four equal sides, so its opposite sides are parallel, which makes it a parallelogram with equal sides.
True
Grade 5 Classifying Worksheet Answer Key: problems 16–20
Problem 16: Shared attributes
Every parallelogram has both pairs of opposite sides parallel, and its opposite sides are equal in length. A rectangle is a parallelogram, so it has both attributes.
Opposite sides parallel; opposite sides equal.
Problem 17: Complete the hierarchy
(a) sits between Trapezoid and the shapes with right angles or equal sides: Parallelogram. (b) is the parallelogram with four equal sides: Rhombus. (c) is both a rectangle and a rhombus: Square.
(a) Parallelogram, (b) Rhombus, (c) Square
Problem 18: Name from measures
Four equal sides with opposite sides parallel make it a rhombus. The angles are not \(90^{\circ}\), so it is not a square.
Rhombus
Problem 19: Pizza box top
It has four right angles and four equal sides, so it is a square. By the hierarchy it is also a rectangle, a rhombus, a parallelogram, and a trapezoid, and every one of these is a quadrilateral.
All six names fit. The most specific is square.
Problem 20: Sort the shapes
A is a square, B is a trapezoid with one pair of parallel sides, C is a rhombus, D is a parallelogram, and E is a rectangle.
Parallelograms have two pairs of parallel sides: A, C, D, and E. Rectangles have four right angles: A and E. Only B has exactly one pair of parallel sides.
Parallelograms: A, C, D, E. Rectangles: A, E. Trapezoid only: B.
Grade 5 Classifying Worksheet Answer Key: problems 21–24
Problem 21: Counterexample
A rhombus has four equal sides but its angles are not right angles.
A rhombus is a counterexample; it is not a square.
Problem 22: Riddles
(a) Opposite sides parallel makes a parallelogram. Equal sides without right angles gives a rhombus.
(b) A rectangle with four equal sides is a square.
(a) Rhombus. (b) Square.
Problem 23: Diego's quadrilateral
A quadrilateral with one pair of parallel sides is a trapezoid; this one is a right trapezoid.
A rectangle needs four right angles and two pairs of parallel sides. Diego’s figure has only two right angles, so it is not a rectangle.
Trapezoid (right trapezoid); not a rectangle.
Problem 24: Triangle categories
An isosceles triangle has at least two equal sides. An equilateral triangle has three equal sides, so it has at least two.
True
How to use this grade 5 classifying worksheet answer key
Read this grade 5 classifying worksheet answer key after trying each problem yourself, and redo any problem you missed.
See every chapter on the Grade 5 math page.