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