Polygon Worksheets - Free Printable
Educational worksheet: Polygon Worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Polygon Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Polygon Worksheets
Let's solve the problem step by step.
We are given a worksheet titled "Properties of Polygons", and we need to list two properties for each polygon shown on the coordinate grid. There are four polygons (Polygon 1 through Polygon 4), each plotted on a coordinate plane with a grid.
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We'll examine each polygon one by one, determine its shape, number of sides, symmetry, angles, side lengths, etc., and then list two properties for each.
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- Shape: A regular pentagon (5 equal sides and angles).
- It is centered around the origin, symmetric.
- All sides appear equal in length, and all internal angles are equal.
- It has rotational symmetry of order 5.
- Coordinates suggest it’s a regular pentagon.
✔ Two Properties:
1. It has 5 equal sides.
2. It is a regular polygon (all sides and angles are equal).
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- Shape: A triangle.
- Looks like an isosceles triangle (two sides equal).
- The base is horizontal, and the apex is at the top.
- Let’s check coordinates:
- Bottom-left: (0, 0)
- Bottom-right: (8, 0)
- Top: (4, 6)
- So, base = 8 units, height = 6 units.
- Two sides from (4,6) to (0,0) and (4,6) to (8,0) are equal → isosceles.
- Not equilateral (sides not all equal).
✔ Two Properties:
1. It is an isosceles triangle (two equal sides).
2. It has a horizontal base and is symmetrical about the vertical line x = 4.
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- Shape: A rectangle.
- Appears to have:
- Bottom-left: (0, 0)
- Bottom-right: (6, 0)
- Top-right: (6, 4)
- Top-left: (0, 4)
- So, width = 6 units, height = 4 units.
- Opposite sides are equal and parallel.
- All angles are 90°.
✔ Two Properties:
1. It is a rectangle (four right angles).
2. It has opposite sides that are equal and parallel.
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- Shape: A regular hexagon.
- Six equal sides and angles.
- Symmetric, looks like a honeycomb shape.
- Centered at origin, with vertices at equal distances from center.
- Regular hexagons can be divided into six equilateral triangles.
✔ Two Properties:
1. It has 6 equal sides.
2. It is a regular polygon (all sides and angles are equal).
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Polygon 1:
1. Has 5 equal sides.
2. Is a regular polygon.
Polygon 2:
1. Is an isosceles triangle.
2. Has a horizontal base and is symmetrical about x = 4.
Polygon 3:
1. Is a rectangle.
2. Has opposite sides equal and parallel.
Polygon 4:
1. Has 6 equal sides.
2. Is a regular polygon.
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These answers are based on visual analysis and geometric reasoning from the coordinate grid. Since this is a standard worksheet, these are the expected responses.
We are given a worksheet titled "Properties of Polygons", and we need to list two properties for each polygon shown on the coordinate grid. There are four polygons (Polygon 1 through Polygon 4), each plotted on a coordinate plane with a grid.
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Step 1: Analyze Each Polygon
We'll examine each polygon one by one, determine its shape, number of sides, symmetry, angles, side lengths, etc., and then list two properties for each.
---
🔹 Polygon 1
- Shape: A regular pentagon (5 equal sides and angles).
- It is centered around the origin, symmetric.
- All sides appear equal in length, and all internal angles are equal.
- It has rotational symmetry of order 5.
- Coordinates suggest it’s a regular pentagon.
✔ Two Properties:
1. It has 5 equal sides.
2. It is a regular polygon (all sides and angles are equal).
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🔹 Polygon 2
- Shape: A triangle.
- Looks like an isosceles triangle (two sides equal).
- The base is horizontal, and the apex is at the top.
- Let’s check coordinates:
- Bottom-left: (0, 0)
- Bottom-right: (8, 0)
- Top: (4, 6)
- So, base = 8 units, height = 6 units.
- Two sides from (4,6) to (0,0) and (4,6) to (8,0) are equal → isosceles.
- Not equilateral (sides not all equal).
✔ Two Properties:
1. It is an isosceles triangle (two equal sides).
2. It has a horizontal base and is symmetrical about the vertical line x = 4.
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🔹 Polygon 3
- Shape: A rectangle.
- Appears to have:
- Bottom-left: (0, 0)
- Bottom-right: (6, 0)
- Top-right: (6, 4)
- Top-left: (0, 4)
- So, width = 6 units, height = 4 units.
- Opposite sides are equal and parallel.
- All angles are 90°.
✔ Two Properties:
1. It is a rectangle (four right angles).
2. It has opposite sides that are equal and parallel.
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🔹 Polygon 4
- Shape: A regular hexagon.
- Six equal sides and angles.
- Symmetric, looks like a honeycomb shape.
- Centered at origin, with vertices at equal distances from center.
- Regular hexagons can be divided into six equilateral triangles.
✔ Two Properties:
1. It has 6 equal sides.
2. It is a regular polygon (all sides and angles are equal).
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✔ Final Answers:
Polygon 1:
1. Has 5 equal sides.
2. Is a regular polygon.
Polygon 2:
1. Is an isosceles triangle.
2. Has a horizontal base and is symmetrical about x = 4.
Polygon 3:
1. Is a rectangle.
2. Has opposite sides equal and parallel.
Polygon 4:
1. Has 6 equal sides.
2. Is a regular polygon.
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These answers are based on visual analysis and geometric reasoning from the coordinate grid. Since this is a standard worksheet, these are the expected responses.
Parent Tip: Review the logic above to help your child master the concept of polygon shapes worksheet.
