7th Grade Math ยท Unit 8
Name a quadrilateral by the property that separates it from the others. A square is a rectangle, a rhombus, and a parallelogram, so square is the most specific of those names.
Trapezoid
A trapezoid has exactly one pair of parallel sides. It is not a parallelogram.
An isosceles trapezoid is a trapezoid whose legs are equal. Its base angles are equal, its diagonals are equal, and it has one line of symmetry.
Parallelogram
A parallelogram has both pairs of opposite sides parallel and equal.
Opposite angles are equal. Consecutive angles are supplementary. The diagonals bisect each other.
Rectangle, rhombus, and square
A rectangle is a parallelogram with four right angles and equal diagonals.
A rhombus is a parallelogram with all sides equal and perpendicular diagonals.
A square is a rectangle and a rhombus, so square is the most specific.
Lines of symmetry
A square has 4. A rectangle that is not a square has 2. A rhombus that is not a square has 2.
An isosceles trapezoid has 1. A parallelogram that is not a rectangle or a rhombus has 0.
Choose the most specific name.
Both pairs of opposite sides are parallel, so it is a parallelogram.
Four right angles make that parallelogram a rectangle.
Rectangle is more specific than parallelogram.
Answer: rectangle
Four right angles make it a rectangle. All sides equal make it a rhombus.
A square is a rectangle and a rhombus, so square is the most specific.
Answer: square
Both pairs of opposite sides are parallel, so it is a parallelogram.
All sides equal make it a rhombus.
Rhombus is more specific than parallelogram.
Answer: rhombus
Exactly one pair of parallel sides is a trapezoid.
It is not a parallelogram.
Answer: trapezoid
Exactly one pair of parallel sides means it is a trapezoid.
Equal legs make it an isosceles trapezoid.
Isosceles trapezoid is more specific than trapezoid.
Answer: isosceles trapezoid
Both pairs of opposite sides are parallel, so it is a parallelogram.
Nothing here says the angles are right or the sides are all equal.
Answer: parallelogram
A parallelogram with four right angles is a rectangle.
Rectangle is more specific than parallelogram.
Answer: rectangle
A parallelogram with all sides equal is a rhombus.
Rhombus is more specific than parallelogram.
Answer: rhombus
A square is a rectangle and a rhombus, so square is the most specific.
Answer: square
Four right angles make this rhombus a rectangle as well.
A square is a rectangle and a rhombus, so square is the most specific.
Answer: square
Four right angles make it a rectangle. All sides equal make it a rhombus.
A square is a rectangle and a rhombus, so square is the most specific.
Answer: square
Say what is the same and what is different.
Same: both are parallelograms.
Different: a rectangle has right angles and equal diagonals. A rhombus has all sides equal and perpendicular diagonals.
A square has both.
Answer: Same: both are parallelograms.
Different: a rectangle has right angles and equal diagonals; a rhombus has all sides equal and perpendicular diagonals.
A square has both.
Same: both have four right angles, equal diagonals, and both are parallelograms
Different: every side of a square is equal, and a square has 4 lines of symmetry. A rectangle that is not a square has only the opposite sides equal, and it has 2 lines of symmetry
Answer: Same: both have four right angles, equal diagonals, and both are parallelograms
Different: every side of a square is equal, and a square has 4 lines of symmetry. A rectangle that is not a square has only the opposite sides equal, and it has 2 lines of symmetry
Same: both have all sides equal, perpendicular diagonals, and both are parallelograms
Different: a square has four right angles and equal diagonals. A rhombus that is not a square does not
Answer: Same: both have all sides equal, perpendicular diagonals, and both are parallelograms
Different: a square has four right angles and equal diagonals. A rhombus that is not a square does not
Same: both have both pairs of opposite sides parallel and equal
Different: a rectangle has four right angles and equal diagonals. A parallelogram does not have to
Answer: Same: both have both pairs of opposite sides parallel and equal
Different: a rectangle has four right angles and equal diagonals. A parallelogram does not have to
Same: both have both pairs of opposite sides parallel, and opposite angles are equal
Different: a rhombus has all sides equal and perpendicular diagonals. A parallelogram does not have to
Answer: Same: both have both pairs of opposite sides parallel, and opposite angles are equal
Different: a rhombus has all sides equal and perpendicular diagonals. A parallelogram does not have to
Same: both are quadrilaterals with at least one pair of parallel sides
Different: a trapezoid has exactly one pair of parallel sides. A parallelogram has both pairs. A trapezoid is not a parallelogram
Answer: Same: both are quadrilaterals with at least one pair of parallel sides
Different: a trapezoid has exactly one pair of parallel sides. A parallelogram has both pairs. A trapezoid is not a parallelogram
Same: both have exactly one pair of parallel sides
Different: an isosceles trapezoid has equal legs, equal base angles, equal diagonals, and one line of symmetry
Answer: Same: both have exactly one pair of parallel sides
Different: an isosceles trapezoid has equal legs, equal base angles, equal diagonals, and one line of symmetry
Same: both have both pairs of opposite sides parallel
Different: a square has four right angles, all sides equal, equal diagonals, and 4 lines of symmetry
Answer: Same: both have both pairs of opposite sides parallel
Different: a square has four right angles, all sides equal, equal diagonals, and 4 lines of symmetry
Same: both have equal diagonals and at least one pair of parallel sides
Different: a rectangle has two pairs of parallel sides and four right angles. An isosceles trapezoid has exactly one pair of parallel sides
Answer: Same: both have equal diagonals and at least one pair of parallel sides
Different: a rectangle has two pairs of parallel sides and four right angles. An isosceles trapezoid has exactly one pair of parallel sides
Same: both have both pairs of opposite sides parallel, and opposite angles are equal
Different: every side of a rhombus is equal. A parallelogram only needs the opposite sides to be equal
Answer: Same: both have both pairs of opposite sides parallel, and opposite angles are equal
Different: every side of a rhombus is equal. A parallelogram only needs the opposite sides to be equal
Same: both have equal diagonals and at least one line of symmetry
Different: a square has two pairs of parallel sides, four right angles, all sides equal, and 4 lines of symmetry. An isosceles trapezoid has exactly one pair of parallel sides and 1 line of symmetry
Answer: Same: both have equal diagonals and at least one line of symmetry
Different: a square has two pairs of parallel sides, four right angles, all sides equal, and 4 lines of symmetry. An isosceles trapezoid has exactly one pair of parallel sides and 1 line of symmetry
Decide what must be true, and count lines of symmetry.
Four right angles would make a rectangle, which has two pairs of parallel sides. All sides equal is not required for a trapezoid.
The statement that must be true is: exactly one pair of parallel sides.
Answer: exactly one pair of parallel sides
All sides equal is true for a square, not for every rectangle. A rectangle has two pairs of parallel sides, not exactly one.
The statement that must be true is: four right angles.
Answer: four right angles
Four right angles would make it a square. A rhombus has two pairs of parallel sides.
The statement that must be true is: all sides equal.
Answer: all sides equal
A square has two pairs of parallel sides and 4 lines of symmetry.
The statement that must be true is: all sides equal.
Answer: all sides equal
All angles equal would make it a rectangle. A parallelogram does not have exactly one pair of parallel sides.
The statement that must be true is: both pairs of opposite sides parallel.
Answer: both pairs of opposite sides parallel
Four right angles and two pairs of parallel sides would make a rectangle, not a trapezoid.
The statement that must be true is: the legs are equal.
Answer: the legs are equal
The two diagonals and the two midlines are lines of symmetry.
The count is 4 lines of symmetry.
Answer: 4
The two midlines work. The diagonals of a rectangle that is not a square do not.
The count is 2 lines of symmetry.
Answer: 2
The two diagonals are lines of symmetry. A rhombus that is not a square does not have the extra midlines a square has.
The count is 2 lines of symmetry.
Answer: 2
One line cuts through the midpoints of the two bases. The legs match across that line.
The count is 1 line of symmetry.
Answer: 1
Opposite sides match, but no fold makes the whole figure land on itself.
The count is 0 lines of symmetry.
Answer: 0
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