Question 1

Explain the progression of the van Hiele levels of geometric understanding. Give an example to illustrate each level.

Accepted Answer

The answer of Explain the progression of the van Hiele...

Question 2

Which of the following triangles can also be an equilateral triangle?
A)acute
B)scalene
C)right
D)obtuse

Accepted Answer

An equilateral triangle has three equal angles of 60 degrees each. An acute triangle has three angles less than 90 degrees, which means all angles are less than 60 degrees. Therefore, an acute triangle can also be an equilateral triangle. A scalene triangle has three sides of unequal length, so it cannot be an equilateral triangle. A right triangle has one angle of 90 degrees and the other two angles add up to 90 degrees, so it cannot be an equilateral triangle. An obtuse triangle has one angle greater than 90 degrees, which means the other two angles are less than 60 degrees, so it cannot be an equilateral triangle.

Question 3

TIMSS: Of the following options, which is NOT true for all rectangles?
A)The opposite sides are parallel.
B)The opposite sides are equal.
C)All angles are right angles.
D)The diagonals are equal.
E)The diagonals are perpendicular.

Accepted Answer

The answer of TIMSS: Of the following options, which is...

Question 4

Which of the following combinations of regular polygons will tessellate?
A)2 squares, 2 triangles
B)2 pentagons, 1 square
C)2 octagons, 1 triangle
D)3 hexagons

Accepted Answer

To tessellate a plane with regular polygons, the sum of the angles around each point must equal 360 degrees. Only regular hexagons have angles that add up to 360 degrees, so any combination of regular hexagons will tessellate the plane. Choice D has 3 hexagons, so it will tessellate. A, B, and C do not have enough hexagons and their other polygons will not tessellate with each other.

Question 5

An octahedron has 8 faces and 6 vertices. It has ___ edges.
A)14
B)12
C)10
D)8

Accepted Answer

An octahedron has 8 triangular faces, which means there are 24 edges in total (each face has 3 edges). However, each edge is shared by exactly 2 faces. Therefore, the number of edges is 24/2 = 12.

Question 6

A seven-sided figure called:
A)a hexagon.
B)a heptagon.
C)a decagon.
D)an octagon.

Accepted Answer

A seven-sided figure is called a heptagon. Hexagon has six sides, decagon has ten sides, and octagon has eight sides.

Question 7

NAEP: Which of the following cannot be folded into a cube?
A) 
B) 
C) 
D)

Accepted Answer

The answer of NAEP: Which of the following cannot be...

Question 8

A parent asks why geometry is taught in the elementary school curriculum when students do not yet know their basic facts and therefore should be spending time on learning them instead. How would you reply to this parent?

Accepted Answer

The answer of A parent asks why geometry is taught...

Question 9

All of the following are true about a parallelogram except:
A)two pairs of parallel sides.
B)two pairs of congruent sides.
C)congruent diagonals.
D)diagonals bisect each other.

Accepted Answer

Parallelograms have two pairs of parallel sides and two pairs of congruent sides, and their diagonals bisect each other, but their diagonals are not necessarily congruent.

Question 10

Why is it important for a child to develop spatial sense?

Accepted Answer

The answer of Why is it important for a child...

Question 11

Explain the differences between congruence and similarity of geometric figures.

Accepted Answer

The answer of Explain the differences between congruence and similarity...

Question 12

Which of the following is true?
A)All squares are rectangles.
B)All rectangles are squares.
C)All parallelograms are rhombuses.
D)All rhombuses are rectangles.

Accepted Answer

A square is a special type of rectangle where all sides are equal in length. Therefore, all squares are also rectangles. However, not all rectangles are squares because they may have different lengths for their opposite sides. Option B is false because, as stated, not all rectangles are squares. Option C is false because while all rhombuses can be parallelograms, not all parallelograms are rhombuses. Option D is false because while all rectangles can be rhombuses if their opposite sides are equal, not all rhombuses are rectangles as their angles may not be 90 degrees.

Question 13

Teacher Licensing Examination Questions
Praxis: In this circle with center O and radius 2, AP has length 3 and is tangent to the circle at P .

If CP is a diameter of the circle, what is the length of AC ?
A)1.3
B)2.0
C)3.2
D)5.0

Accepted Answer

The answer of Teacher Licensing Examination Questions
Praxis: In this circle...

Question 14

Give four different types of manipulatives you could use to introduce geometric concepts to elementary children. Explain how these help children to understand these concepts.

Accepted Answer

The answer of Give four different types of manipulatives you...

Question 15

What are some activities you could use to introduce children to three-dimensional geometry? Explain how these activities encourage the development of these geometric concepts.

Accepted Answer

The answer of What are some activities you could use...

Question 16

The following translation will move point Q from (3, − 4)to ______.

A)(6, 1)
B)(0, 9)
C)(0, 1)
D)(6, 9)

Accepted Answer

The answer of The following translation will move point Q...

Question 17

Explain the differences between the four geometry systems that are taught in the elementary school curriculum (topological, Euclidean, transformational, and coordinate geometry).

Accepted Answer

The answer of Explain the differences between the four geometry...

Question 18

How many lines of symmetry are there in a regular hexagon?
A)3
B)4
C)6
D)8

Accepted Answer

A regular hexagon has 6 equal sides and 6 equal angles, and therefore has 6 lines of symmetry that divide the hexagon into two congruent parts.

Question 19

What is the area of a figure on a grid with 12 interior points and 8 boundary points?
A)15
B)19
C)13
D)14

Accepted Answer

The area can be calculated using Pick's Theorem: Area = I + B/2 - 1, where I is the number of interior points and B is the number of boundary points. Substituting the given values: Area = 12 + 8/2 - 1 = 15.

Question 20

The legs of a right triangle are 5 cm and 12 cm. The length of the third side is:
A)17 cm.
B)13 cm.
C)60 cm.
D)119 cm.

Accepted Answer

The third side of a right triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, if the legs are 5 cm and 12 cm, the length of the hypotenuse is the square root of (5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13 cm.

Quiz 16: Developing and Extending Geometric Concepts and Systems

Explain the progression of the van Hiele levels of geometric understanding. Give an example to illustrate each level.

Which of the following triangles can also be an equilateral triangle?

TIMSS: Of the following options, which is NOT true for all rectangles?

Which of the following combinations of regular polygons will tessellate?

An octahedron has 8 faces and 6 vertices. It has ___ edges.

A seven-sided figure called:

NAEP: Which of the following cannot be folded into a cube?

A parent asks why geometry is taught in the elementary school curriculum when students do not yet know their basic facts and therefore should be spending time on learning them instead. How would you reply to this parent?

All of the following are true about a parallelogram except:

Why is it important for a child to develop spatial sense?

Explain the differences between congruence and similarity of geometric figures.

Which of the following is true?

Teacher Licensing Examination Questions Praxis: In this circle with center O and radius 2, AP has length 3 and is tangent to the circle at P . If CP is a diameter of the circle, what is the length of AC ?

Give four different types of manipulatives you could use to introduce geometric concepts to elementary children. Explain how these help children to understand these concepts.

What are some activities you could use to introduce children to three-dimensional geometry? Explain how these activities encourage the development of these geometric concepts.

The following translation will move point Q from (3, − 4) to ______.

Explain the differences between the four geometry systems that are taught in the elementary school curriculum (topological, Euclidean, transformational, and coordinate geometry).

How many lines of symmetry are there in a regular hexagon?

What is the area of a figure on a grid with 12 interior points and 8 boundary points?

The legs of a right triangle are 5 cm and 12 cm. The length of the third side is: