Shape Properties - ISEE Lower Level Quantitative Reasoning

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Question

A two-dimensional figure has four sides, the length is 3 centimeters. All of its four angles are right angles. Choose the correct category (or categories) that describes this type of figure.

Answer

No explanation available

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Question

Which of the following shapes is NOT a quadrilateral?

Answer

A quadrilateral is any two-dimensional shape with sides. The only shape listed that does not have sides is a triangle.

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Question

What other shape can a parallelogram be classified as?

Answer

A parallelogram can not be classified as a square because a square has to have equal sides, but a parallelogram can have two different side lengths, as long as the opposite side lengths are equal.

A parallelogram can not be classified as a rectangle because a rectangle has to have angles, and a parallelogram does not.

A parallelogram can not be classified as a triangle because a parallelogram has to have sides and a triangle only has sides.

A parallelogram can not be classified as a rhombus because a rhombus has to have equal sides and a parallelogram does not.

A parallelogram has four sides, and all shapes with four sides are quadrilaterals.

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Question

What is the main difference between a square and a rectangle?

Answer

The only difference between a rectangle and a square is their side lengths. A square has to have equal side lengths, but the opposite side lengths of a rectangle only have to be equal.

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Question

What two shapes can a square be classified as?

Answer

A square can also be a rectangle and a rhombus because a rectangle has to have at least sets of equal side lengths and a rhombus has to have equal side lengths, like a square, and at least sets of equal angles.

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Question

What is the main difference between a triangle and a rectangle?

Answer

Out of the choices given, the only characteristic used to describe shapes is the number of sides. A triangle has sides and a rectangle has sides.

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Question

Which two shapes have to have right angles?

Answer

By definition, the only two quadrilaterals that have to have right angles, are the square and the rectangle.

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Question

What is the main difference between a right triangle and an isosceles triangle?

Answer

By definition, a right triangle has to have one right angle, or a angle, and an isosceles triangle has equal base angles and two equal side lengths.

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Question

Which of the shapes is NOT a quadrilateral?

Answer

A quadrilateral is a sided shape. The only shape listed that does not have sides is a hexagon, which has sides.

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Question

What is the difference between an equilateral triangle and a scalene triangle?

Answer

Of the choices listed, the main difference between an equilateral triangle and a scalene triangle is their side lengths. An equilateral triangle has to have equal sides, but a scalene triangle can have all different side lengths.

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Question

Which of the following shapes is NOT a parallelogram?

Answer

A rectangle, square, and rhombus can all be classified as a parallelogram because each shape has opposite side lengths that are equal. A kite does not.

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Question

What is the difference between a trapezoid and a isosceles trapezoid?

Answer

By definition, an isosceles trapezoid has to have equal base angles, but a trapezoid does not have to have equal angles.

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Question

Which shape is NOT a quadrilateral?

Answer

A quadrilateral has to have sides, a circle does not have any sides.

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Question

Which shape can have all sides of varying length?

Answer

A quadrilateral has to have side lengths, but they can all cary in size.

A square has equal sides.

A rectangle and parallelogram have opposite, equal side lengths.

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Question

Which shape has only one pair of opposite, equal angles?

Answer

A kite has to one one set of opposite, equal angles.

A square and a rectangle have equal angles.

A parallelogram has two sets of opposite, equal angles.

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Question

Which shape has two pairs of adjacent sides, with the adjacent sides being equal in length?

Answer

A kite has two sets of adjacent sides, and the adjacent sides have equal lengths.

A rectangle, parallelogram, and trapezoid do not have adjacent sides that are qual in length.

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Question

Which shape can have sides of any length, but has to have one set of parallel sides?

Answer

A trapezoid can have sides of any length, but one set of sides have to be parallel.

Both a square and a rectangle cannot have sides of any length.

A quadrilateral can have sides of any length, but it does not have to have a pair of sides that are parallel.

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Question

Which shape can have angles of all different degrees?

Answer

A trapezoid can have angles of all different degrees.

A square and a rectangle have to have all equal angles.

A parallelogram has to have opposite, equal angles.

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Question

Which shape has two sets of opposite sides that are equal in length and also parallel?

Answer

A parallelogram has two sets of opposite sides that are equal in length and parallel.

A trapezoid and a quadrilateral can have sides of any length.

A kite does not have any sets of parallel sides.

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Question

Which shape has two sets of opposite, equal angles?

Answer

A parallelogram has two sets of opposite, equal angles.

A kite has to one one set of opposite, equal angles.

A quadrilateral and trapezoid do not have to have any equal angles.

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