Which statements about the quadrilaterals must be true?


To answer which statements about quadrilaterals must be true, let’s first review some key properties of quadrilaterals:

### General properties of all quadrilaterals:
1. A quadrilateral has **four sides**.
2. The sum of the interior angles of a quadrilateral is **360°**.

However, if you're referring to specific types of quadrilaterals, here are some statements that must be true for certain categories:

### For **parallelograms**:
- Opposite sides are **parallel** and **equal in length**.
- Opposite angles are **equal**.
- Diagonals **bisect** each other.

### For **rectangles** (a type of parallelogram):
- All angles are **right angles (90°)**.
- Diagonals are **equal in length**.

### For **rhombuses** (a type of parallelogram):
- All sides are **equal in length**.
- Diagonals **bisect each other at right angles**.

### For **squares** (a special type of both rectangle and rhombus):
- All sides are **equal**, and all angles are **right angles**.
- Diagonals are **equal** and **bisect each other at right angles**.

### For **trapezoids (trapeziums)**:
- **One pair of opposite sides** is **parallel**.

### True Statements (Generalized):
1. The sum of the interior angles of any quadrilateral is **360°**.
2. In a parallelogram, opposite sides are **equal and parallel**.
3. In a rectangle, all angles are **90°**.
4. In a rhombus, all sides are **equal in length**.
5. In a square, diagonals are **equal** and **bisect at right angles**.

Would you like further explanation on any of these properties?

### Questions for further understanding:
1. How do the diagonals of a parallelogram behave compared to other quadrilaterals?
2. What is the relationship between the sides of a rhombus and a rectangle?
3. How do you calculate the area of a trapezoid given its dimensions?
4. Can a quadrilateral have unequal diagonals but equal side lengths?
5. What is a cyclic quadrilateral

Which statements about the quadrilaterals must be true?

Explore the key properties and true statements about different types of quadrilaterals, such as parallelograms, rectangles, rhombuses, and squares. Learn about their angles, sides, and diagonals with clear explanations, perfect for Grades 6-8 geometry students.

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