A rhombus is a four-sided figure with all sides of the same length. Here are three examples. Which of the following is not true in every rhombus?

The two diagonals have the same length.

Each diagonal bisects two angles of the rhombus.

The two diagonals are perpendicular.

The opposite angles have the same measure.

All of the above are true in every rhombus.

An isosceles triangle is a triangle with two sides of equal length. Here are three examples. Which of the following is true of every isosceles triangle?

There must be at least two angles with the same measure.

The three sides must have the same length.

One side must have twice the length of another side.

The three angles must have the same measure.

None of the above is true in every isosceles triangle.

Two circles with centers P and Q intersect at R and S to form a four-sided figure PQRS. Here are two examples. Which of the following is not always true?

Angles P and Q will have the same measure.

PQRS will have two pairs of sides of equal length.

PQRS will have at least two angles of equal measure.

The lines PQ and RS will be perpendicular.

Here are two statements. Which is correct?

Statements S and T cannot both be true.

Which of these can be called rectangles?

All of the above are rectangles.

All properties of rectangles are properties of all squares.

All properties of squares are properties of all rectangles.

All properties of rectangles are properties of all parallelograms.

All properties of squares are properties of all parallelograms.

What do all rectangles have that some parallelograms do not have?

The opposite sides are parallel.

Here is a right triangle ABC. Equilateral triangles ACE, ABF and BCD have been constructed on the sides of ABC. From this information, one can prove that AD, BE and CF have a point in common. What would this proof tell you?

In any right triangle, AD, BE and CF have a point in common.

Only in this triangle drawn can we be sure that AD, BE and CF have a point in common.

In some but not all right triangles, AD, BE and CF have a point in common.

In any triangle, AD, BE and CF have a point in common.

In any equilateral triangle, AD, BE and CF have a point in common.

Here are two statements. Which is correct?

To prove II is false, it is enough to find one non-rectangle whose diagonals bisect each other.

To prove I is true, it is enough to prove that II is true.

To prove II is true, it is enough to prove that I is true.

To prove II is true, it is enough to find one rectangle whose diagonals bisect each other.

some terms must be left undefined, and it is necessary to have some statements which are assumed true.

every term can be defined and every true statement can be proved true.

every term can be defined, but it is necessary to assume that certain statements are true.

some terms must be left undefined, but every true statement can be proved true.

None of the above statements is correct.

In F-geometry, one that is different from the one you are used to, there are exactly four points and six lines. every line contains exactly two points. If the points are P, Q, R and S, the lines are {P, Q}, {P, R}, {P, S}, {Q, R}, {Q, S} and {R, S}. Here are how the words "intersect" and "parallel" are used in F-geometry. The lines {P, Q} are {P, R} intersect at P because {P, Q} and {P, R} have P in common. The lines {P, Q} and {R, S} are parallel because they have no points in common. From this information, which of the following is correct?

{P, R} and {Q, S} are parallel.

{Q, R} and {R, S} are parallel.

To trisect an angle means to divide it into three parts of equal measure. In 1847, P.L. Wantzel proved that, in general, it is impossible to trisect angles using only a compass and unmarked ruler. From this proof, what can you conclude?

No one will ever be able to find a general method for trisecting angles using only a compass and an unmarked ruler.

In general, it is impossible to bisect angles using only a compass and an unmarked ruler.

In general, it is impossible to trisect angles using only a compass and a marked ruler.

In general, it is impossible to trisect angles using any drawing instruments.

It is still possible that in the future someone may find a general way to trisect angles using only a compass and an unmarked ruler.

There is a geometry invented by a mathematician J in which the following is true: The sum of the measures of the angles of a triangle is less than 180 degrees. Which is correct?

J started with different assumptions than those in the usual geometry.

J made a mistake in measuring the angles of the triangle.

J made a mistake in logical reasoning.

J has a wrong idea of what is meant by "true."

Two geometry books define the word rectangle in different ways. Which is true?

The rectangles in one of the books must have the same properties as those in the other book.

One of the definitions is wrong. There cannot be two different definitions for rectangle.

The rectangles in one of the books must have different properties from those in the other book.

The properties of rectangles in the two books might be different.

van Hiele Test

Authored by Todd Moyer

Mathematics

8th Grade - University

CCSS covered

Used 171+ times

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25 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of these are squares?

K only

L only

M only

L and M only

All are squares

Tags

CCSS.3.G.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of these are triangles?

None of these are triangles.

V only

W only

W and X only

V and W only

Tags

CCSS.2.G.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of these are rectangles?

S only

T only

S and T only

S and U only

All are rectangles.

Tags

CCSS.5.G.B.4

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of these are squares?

None of these are squares.

G only

F and G only

G and I only

All are squares.

Tags

CCSS.3.G.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of these are parallelograms?

J only

L only

J and M only

None of these are parallelograms.

All are parallelograms.

Tags

CCSS.2.G.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which relationship is true in all squares?

PR and PS have the same length.

QS and PR are perpendicular.

PS and QR are perpendicular.

PS and QS have the same length.

Angle Q is larger than angle R.

Tags

CCSS.HSG.CO.C.11

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of the following is not true in every rectangle?

There are four right angles.

There are four sides.

The diagonals have the same length.

The opposite sides have the same length.

All of the above are true in every rectangle.

Tags

CCSS.HSG.CO.C.11

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