Geometry Cheat Sheet - Free Printable

It looks like you've uploaded a "Geometry Quick Guide 2: 2D Shapes" reference sheet, which is a helpful visual guide for identifying and understanding different types of two-dimensional shapes. However, there isn't an actual problem or task included in the image — it's just a summary chart.

Let me break down what this guide contains and how it can be used:

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🔍 Overview of the Guide

This chart categorizes 2D shapes into three main groups:
1. Triangles
2. Quadrilaterals
3. Regular Polygons

Each shape includes:
- A diagram
- Name
- Key properties (side lengths, angles, symmetry)

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📐 1. Triangles

| Shape | Properties |
|------|------------|
| Equilateral triangle | All sides equal; all interior angles = 60° |
| Isosceles triangle | Two equal sides; two congruent angles |
| Scalene triangle | No equal sides or angles |
| Right triangle | One 90° angle |
| Acute triangle | All angles < 90° |
| Obtuse triangle | One angle > 90° |

> ✔ Tip: The sum of interior angles in any triangle is always 180°.

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🔶 2. Quadrilaterals

| Shape | Properties |
|------|------------|
| Square | All sides equal; all angles = 90° |
| Rectangle | Opposite sides equal; all angles = 90° |
| Rhombus | All sides equal; opposite angles equal; two pairs of parallel lines |
| Parallelogram | Opposite sides equal and parallel; opposite angles equal |
| Kite | Two pairs of adjacent equal sides; one pair of congruent angles |
| Trapezoid | One pair of parallel sides (US definition) |
| Trapezium | No parallel sides (UK definition; sometimes reversed in US) |

> ⚠️ Note: Definitions of "trapezoid" and "trapezium" vary by region!

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🔷 3. Regular Polygons

These are polygons with all sides and angles equal.

| Shape | Sides | Interior Angle |
|-------|-------|----------------|
| Equilateral Triangle | 3 | 60° |
| Square | 4 | 90° |
| Regular Pentagon | 5 | 108° |
| Regular Hexagon | 6 | 120° |
| Regular Octagon | 8 | 135° |
| Regular Decagon | 10 | 144° |

> 🔁 Formula for interior angle of a regular polygon:
> $$
> \text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n}
> $$
> where $ n $ = number of sides.

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💡 How to Use This Guide

This guide is useful for:
- Identifying shapes based on their properties
- Solving geometry problems involving angles and side lengths
- Preparing for exams or homework
- Teaching basic geometry concepts

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❓ What Can You Do With It?

Since no specific problem was given, here’s an example task you might solve using this guide:

#### Example Problem:
> A quadrilateral has four equal sides and two pairs of parallel lines. What shape is it?

✔ Solution:
From the guide → Look under Quadrilaterals:
- Rhombus: All sides equal; 2 pairs of parallel lines → ✔️ Matches!
- But wait: Square also has these properties! So both could fit?

But note: A square has all angles = 90°, while a rhombus doesn’t necessarily. If no info about angles is given, it's a rhombus.

So unless specified as having right angles, the answer is: Rhombus.

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✔ Summary

This guide is not a problem to solve but a reference tool. To use it effectively:

- Match descriptions to diagrams.
- Use formulas for angles in regular polygons.
- Know the differences between similar shapes (e.g., rectangle vs. rhombus).

If you have a specific question or problem related to this guide (like “What is the missing angle in this triangle?”), please share it, and I’ll help solve it step-by-step!