Practice questions for Unit 1
Which of the following shapes always have two pairs of opposite parallel sides? a. Square b. Rectangle c. Rhombus d. Parallelogram e. Kite f. Exclusive Trapezoid
a. Square b. Rectangle c. Rhombus d. Parallelogram
A rectangle is_____ a parallelogram
always
A square is _______ a rectangle
always
A quadrilateral with 2 sets of adjacent congruent sides and at least one pair of opposite congruent angles. Has at least one line of symmetry
Kite
Draw a correct Venn diagram to show the relationship between a kite, rhombus, and square.
Kite--->Rhombus--->Square
What properties of the diagonals of a quadrilateral would guarantee that it is a parallelogram?
The diagonals bisect each other.
A rhombus is always, sometimes, or never a kite
Always
A square is always sometimes or never a trapezoid
Always- 4 congruent sides, 4 parallel sides
9. With a single cut, a rectangle is cut into two pieces. Which of the following shapes could the two pieces be? If it is possible, draw it. a. Two congruent right triangles
Drawing of a rectangle cut with one diagnal
b. Two trapezoids that are not rectangles
Drawn in the middle-ish
What can a trapezoid do that a parallelogram cant?
Have different angle and side measurements
At what minimum van Hiele level are the following students operating? b. Doug makes a correct hierarchy diagram to show the relationship between different kinds of triangles.
Level 2
Consider the following statement: "If the angles of a quadrilateral are all congruent, then the quadrilateral must be a square." Is this correct? Why or why not
No, it is not correct. A quadrilateral with angles that are all congruent could be a square, but it also could be a rectangle that isn't a square.
c. Two equilateral triangles
Not possible. Equilateral triangles have angles that all measure 60°. If a rectangle is cut into two triangles, each triangle will have one right angle.
what can a rectangle do that a parallelogram cant?
Nothing
Shape with 2 sets of opposite congruent sides and opposite congruent angles
Parallelogram
Venn diagram that depicts parallelogram, rhombus, and rectangle
Parallelogram--->Rectangle&Rhombus
Quadrilateral with 4 sets of right angles and 2 sets of opposite congruent sides
Rectangle
An equilateral quadrilateral parallelogram
Rhombus
What shapes are part of the kite family?
Rhombus and square
What is the best name for a quadrilateral that has the property that all four interior angles are bisected by its diagonals
Rhombus.
A kite is ___ a square
Sometimes
A rectangle is sometimes, always, or never a rhombus
Sometimes
A rectangle is always, sometimes, or never a kite
Sometimes- when its a square
What can a rhombus do that a rectangle cant?
change its angle sizes
What does a trapezoid have in common with the parallelogram family?
They can have parallel lines, but they dont have to
Draw a correct hierarchy diagram to show the relationship between an inclusive trapezoid, kite, parallelogram, and rhombus.
Trapezoid-->Parallelogram--> Rhombus<--Kite
What is the ultimate venn diagram?
Trapezoid-->Parallelogram-->rectangle-->square<---Rhombus<---Kite
Draw a venn diagram relating Kite, trapezoid, and rhombus
Trapezoid-->Rhombus<--Kite
draw a venn diagram relating trapezoid, square, parallelogram and rhombus
Trapezoid-->parallelogram--->rhombus--->square
T/F Some rectangles are squares, and some rectangles are not squares
True
T/F Some right triangles are isosceles and some are not
True
T/F Some scalene triangles are acute and some are not
True
Is it possible to draw a parallelogram that is also a kite? Explain why or why not.
Yes, by drawing a rhombus, which is a kite and a parallelogram.
What can a rectangle do that a rhombus cant?
doesnt have to be equilateral
At what minimum van Hiele level are the following students operating? a. Frances sees the two shapes below. She recognizes that the one of the right is a rectangle, but doesn't know what the one on the left is. / --
level 0
Children recognize shapes in terms of their wholes and what they resemble. They recognize a square when its a box, but not when its turned to look like a diamond. They say diamond.
level 0:visualization
Recognize shape properties. They see how parallel lines are parallel, but dont see how they are equal in size
level 1: analysis
Children can deduce shapes and see how they are related in their properties. They can form minimal lists and hierarchy of shapes.
level 2: informal deduction
An equilateral triangle is ___ an isosceles triangle
never
Does the definition of a parallelogram always meet the definition of a rectangle?
no
What can a kite do that a trapezoid cant?
not have parallel sides and adjacent angles dont have to be supplementary
What can a parallelogram do that a trapezoid cant?
nothing
what can a rhombus do that a parallelogram cant?
nothing
Inclusive trapezoid
quadrilateral with at least one pair of parallel sides
Exclusive trapezoid
quadrilateral with only one pair of opposite sides
A kite is ____ a rhombus
sometimes
A rhombus is sometimes, always, or never a rectangle
sometimes
An acute triangle is____ a scalene triangle
sometimes
An isosceles triangle is _____ a right triangle
sometimes
A rhombus is ____ a rectangle
sometimes (when its a square)
A trapezoid is always, sometimes, or never a rhombus
sometimes- sides dont have to be parallel
A kite is____ a trapezoid
sometimes- when its a rhombus or square
Does the definition of a rectangle always meet the definition of a parallelogram?
yes
