Testinar Grade 5 math

Classifying Triangles and Quadrilaterals

Students will classify triangles and quadrilaterals using properties and hierarchy.

CH10-06 Geometry and Coordinate Plane

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

Which figure is described as having exactly one pair of parallel sides and is not a parallelogram?
1. Figure A
2. Figure B
3. Figure C
4. Figure D
Which statement is true?
1. A square is always a rectangle.
2. A rectangle is always a square.
3. A trapezoid is always a parallelogram.
4. A rhombus is never a square.
Which statement correctly explains the relationship between squares and rectangles?
1. Every square is a rectangle because it has four right angles and two pairs of parallel sides.
2. Every rectangle is a square because it has four right angles.
3. No square is a rectangle because a square has all sides equal.
4. A square is not a quadrilateral because it has four equal sides.
Which figure is a parallelogram?
1. Figure A
2. Figure B
3. Figure C
4. Figure D
Every rhombus must have:
1. Four right angles
2. Four equal sides
3. Only one pair of parallel sides
4. Four different side lengths
According to the hierarchy, which is true?
1. Every rectangle is a square.
2. Every parallelogram is a trapezoid.
3. Every trapezoid is a parallelogram.
4. Every square is a rectangle.
Which attribute does NOT belong to every rectangle?
1. Four sides
2. All angles are \(90^\circ\)
3. All sides are equal
4. Opposite sides are parallel
A quadrilateral has exactly one pair of parallel sides. What is the most specific name for this figure?
1. Rectangle
2. Rhombus
3. Trapezoid
4. Square

Teacher and parent reference

Answer key and explanations

B. Figure B
Figure B is described as having exactly one pair of parallel sides, so it is not a parallelogram. Figures A and D are in the parallelogram family because they have two pairs of parallel sides.
A. A square is always a rectangle.
A square has four right angles and opposite sides parallel, so it meets the definition of a rectangle. A square is a special type of rectangle.
A. Every square is a rectangle because it has four right angles and two pairs of parallel sides.
A square has all the properties of a rectangle: four right angles and two pairs of parallel sides. A rectangle does not need to have all four sides equal, so not every rectangle is a square.
D. Figure D
A parallelogram has two pairs of parallel sides. Figure D has two pairs of opposite sides parallel; Figures A, B, and C do not.
B. Four equal sides
A rhombus is a quadrilateral with all four sides equal in length. It does not have to have four right angles.
D. Every square is a rectangle.
The hierarchy shows that Square is a child of Rectangle, meaning every square is also a rectangle. Not every rectangle is a square.
C. All sides are equal
A rectangle must have four right angles and opposite sides parallel, but the sides do not have to all be equal. A square has all equal sides, but a rectangle does not.
C. Trapezoid
Using this definition, a quadrilateral with exactly one pair of parallel sides is a trapezoid. Rectangles, rhombuses, and squares have two pairs of parallel sides.