ISEE Lower Level Mathematics Achievement Quiz: Identifying Polygons

What this quiz covers

This quiz focuses on Identifying Polygons, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. Every rectangle is also a square.
2. Every rhombus is also a square.
3. Every square is also a rectangle. (correct answer)
4. Every trapezoid is also a parallelogram.

Explanation: A square has all the properties of a rectangle (four right angles, two pairs of parallel sides) plus the additional property of having four equal sides. Therefore, every square is a rectangle. The other statements are not always true; for example, a rectangle is only a square if its sides are equal.

Question 2

1. Circle
2. Oval
3. Square (correct answer)
4. Ring

Explanation: This question tests the ISEE Lower Level skill of identifying polygons based on their properties. A polygon is defined as a flat shape with straight sides, which is the key distinction being tested here. Students must identify which shape has straight sides rather than curved edges. The correct answer is C (Square) because a square is a polygon with four straight sides, while circles, ovals, and rings all have curved edges and are not polygons. This question helps students understand the fundamental difference between polygons and non-polygons. Teaching strategies include having students sort shapes into two groups: those with straight sides (polygons) and those with curved edges (non-polygons). Emphasize that the word 'polygon' means 'many angles' and that curved shapes have no angles.

Question 3

1. Rectangle
2. Triangle
3. Square (correct answer)
4. Pentagon

Explanation: This question tests the ISEE Lower Level skill of identifying polygons based on their properties. A polygon is defined as a flat shape with straight sides, and this question combines two important properties: having four sides and having all sides equal. The shape that has four equal sides and four angles is a square, which is a special type of quadrilateral. The correct answer is C (Square) because squares are defined by having four sides of equal length and four right angles. A common distractor is rectangle, which has four sides and four angles but only opposite sides are equal, not all four. Teaching strategies include having students use rulers to verify that all four sides of a square are equal, unlike rectangles. Emphasize that while all squares are rectangles, not all rectangles are squares.

Question 4

1. Square
2. Triangle
3. Rectangle (correct answer)
4. Circle

Explanation: This question tests the ISEE Lower Level skill of identifying polygons based on their properties. A polygon is defined as a flat shape with straight sides, and different four-sided polygons (quadrilaterals) have different properties regarding their side lengths. The question asks for a shape with four sides where not all sides are equal, which describes a rectangle. The correct answer is C (Rectangle) because rectangles have four sides with opposite sides equal, but not all four sides equal like a square. Common distractors include squares (all sides equal) and triangles (only three sides), while circles are not polygons. Teaching strategies include having students compare squares and rectangles side by side, measuring to verify that rectangles have two pairs of equal sides rather than four equal sides. Emphasize that both squares and rectangles are quadrilaterals, but they differ in their side length properties.

Question 5

1. Hexagon
2. Rectangle
3. Pentagon (correct answer)
4. Triangle

Explanation: This question tests the ISEE Lower Level skill of identifying polygons based on their properties. A polygon is defined as a flat shape with straight sides and angles, where the number of angles always equals the number of sides. The question specifically asks about angles rather than sides, testing whether students understand this relationship. The correct answer is C (Pentagon) because pentagons have five angles (and five sides). Common distractors include hexagons (6 angles), rectangles (4 angles), and triangles (3 angles). Teaching strategies include having students mark each angle of a polygon with a dot and count them, then verify by counting the sides. Reinforce that 'penta-' means five, just as a pentagon building has five sides.

Question 6

1. Triangle (correct answer)
2. Pentagon
3. Hexagon
4. Circle

Explanation: This question tests the ISEE Lower Level skill of identifying polygons based on their properties. A polygon is defined as a flat shape with straight sides and angles, with the simplest polygon being a triangle. The question asks students to identify which shape has three sides and three angles, reinforcing that sides and angles are always equal in number. The correct answer is A (Triangle) because triangles are defined as having exactly three sides and three angles. Common distractors include pentagons (5 sides/angles) and hexagons (6 sides/angles), while circles have no sides or angles. Teaching strategies include having students draw triangles and mark each side and angle, counting to verify there are three of each. Use everyday examples like yield signs or musical triangles to reinforce this concept.

Question 7

1. Rectangle
2. Square (correct answer)
3. Triangle
4. Pentagon

Explanation: This question tests the ISEE Lower Level skill of identifying polygons based on their properties. A polygon is defined as a flat shape with straight sides, and some polygons have special properties like having all sides equal in length. The question specifically asks for a polygon with four equal sides, which is a defining characteristic of a square. The correct answer is B (Square) because a square is the only four-sided polygon where all sides must be equal in length. A common distractor is rectangle (choice A), which has four sides but only opposite sides are equal, not all four sides. Teaching strategies include using manipulatives like pattern blocks or having students measure the sides of different quadrilaterals with rulers. Watch for confusion between squares and rectangles, as both are four-sided polygons but have different side length properties.

Question 8

1. Triangle (correct answer)
2. Square
3. Pentagon
4. Circle

Explanation: This question tests the ISEE Lower Level skill of identifying polygons based on their properties. A polygon is defined as a flat shape with straight sides, and the most basic polygon is a triangle with three sides. The question directly states that a triangle has three sides and asks students to identify it from the choices. The correct answer is A (Triangle) because triangles are defined as polygons with exactly three sides. Common distractors include squares (4 sides) and pentagons (5 sides), while circles are not polygons since they have curved edges. Teaching strategies include starting with triangles as the simplest polygon and having students find triangular shapes in their environment. Use the prefix 'tri-' to help students remember that triangles have three sides, just as tricycles have three wheels.

Question 9

1. Triangle
2. Pentagon (correct answer)
3. Rectangle
4. Circle

Explanation: This question tests the ISEE Lower Level skill of identifying polygons based on their properties. A polygon is defined as a flat shape with straight sides, and polygons are named based on the number of sides they have, such as triangles (3 sides), pentagons (5 sides), and hexagons (6 sides). In this question, students must identify which shape has exactly five sides. The correct answer is B (Pentagon) because a pentagon is specifically defined as a polygon with five sides. Common distractors include triangles (3 sides) and rectangles (4 sides), while circles are not polygons at all since they have curved edges rather than straight sides. Teaching strategies include having students count the sides of various shapes and create a reference chart matching polygon names to their number of sides. Watch for students who confuse the prefixes (tri-, penta-, hexa-) or who include non-polygons like circles in their answers.

Question 10

1. A rectangle (correct answer)
2. A rhombus
3. A square
4. A kite

Explanation: A parallelogram with four right angles is the definition of a rectangle. It could be a square if the sides are also equal, but it must be at least a rectangle. A rhombus does not necessarily have right angles.

Question 11

1. A regular hexagon
2. A regular octagon (correct answer)
3. A pentagon
4. A square

Explanation: A standard stop sign has 8 equal sides and 8 equal angles, which makes it a regular octagon.

Question 12

1. A hexagon
2. A heptagon (correct answer)
3. An octagon
4. A nonagon

Explanation: A polygon with 7 vertices must also have 7 sides. A polygon with 7 sides is called a heptagon. A hexagon has 6 sides, an octagon has 8, and a nonagon has 9.

Question 13

1. A rhombus
2. A trapezoid
3. A parallelogram
4. A rectangle (correct answer)

Explanation: The description of two pairs of parallel sides and four right angles defines a rectangle. While it is also a parallelogram and a trapezoid, rectangle is the most specific and accurate description.

Question 14

1. A square
2. A trapezoid
3. A rhombus (correct answer)
4. A kite

Explanation: A rhombus is a quadrilateral with four equal sides. A square also has four equal sides, but it must have 90-degree angles. Since the tile has no 90-degree angles, it is a rhombus but not a square.

Question 15

1. An equilateral triangle
2. An isosceles triangle (correct answer)
3. A scalene triangle
4. A right triangle

Explanation: A triangle with at least two sides of equal length is called an isosceles triangle. Since two sides are 5 inches long, this is the correct classification. An equilateral triangle has all three sides equal. A scalene triangle has no sides equal. We don't have enough information to know if it's a right triangle.

Question 16

1. A square
2. A trapezoid
3. A parallelogram (correct answer)
4. A rhombus

Explanation: A quadrilateral with two pairs of parallel sides is a parallelogram. Since the distances between opposite sides are different, the adjacent side lengths are unequal, so it cannot be a square or a rhombus. A trapezoid has only one pair of parallel sides.

Question 17

1. An isosceles trapezoid (correct answer)
2. A general trapezoid
3. A parallelogram
4. A kite

Explanation: When you encounter a question about quadrilaterals, focus on the specific properties given and match them to the most precise geometric name possible. Let's analyze what we know about this bridge support beam: it has one pair of parallel sides (top and bottom) and two non-parallel sides that are equal in length. A quadrilateral with exactly one pair of parallel sides is called a trapezoid. But we have additional information—the two non-parallel sides (called legs) are equal in length. When a trapezoid has equal legs, it's specifically called an isosceles trapezoid. Choice A is correct because an isosceles trapezoid perfectly matches all the given properties: one pair of parallel sides and two equal non-parallel sides. Choice B is incorrect because while the shape is indeed a trapezoid, "general trapezoid" isn't the most specific name. Since we know the legs are equal, we should use the more precise term "isosceles trapezoid." Choice C is wrong because a parallelogram requires two pairs of parallel sides. Our shape only has one pair of parallel sides, so it cannot be a parallelogram. Choice D is incorrect because a kite has two pairs of adjacent sides that are equal, but no parallel sides are required. Our bridge beam specifically has parallel sides, which doesn't match a kite's definition. Always choose the most specific geometric name that fits all given properties. When you see "equal legs" mentioned with a trapezoid, immediately think "isosceles trapezoid."

Question 18

1. A rhombus
2. An isosceles triangle
3. A parallelogram
4. A rectangle (correct answer)

Explanation: A rectangle is defined as a quadrilateral with four right angles. A rhombus, isosceles triangle, and parallelogram can all exist without having any right angles.

Question 19

1. A rectangle
2. A square
3. A parallelogram (correct answer)
4. A trapezoid

Explanation: The properties described—four sides, opposite sides parallel and equal, and no right angles—perfectly match the definition of a parallelogram that is not a rectangle or square. A rectangle or square would have right angles. A trapezoid only has one pair of parallel sides.

Question 20

1. A three-sided figure with equal side lengths.
2. A five-sided figure with unequal side lengths.
3. A four-sided figure with one curved side. (correct answer)
4. A six-sided figure with two right angles.

Explanation: A key property of a polygon is that all of its sides must be straight line segments. A figure with a curved side cannot be a polygon.