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Chapter 7: Problem 4

Complete the following definitions and theorems. Each angle of a rectangle is a.

Short Answer

Expert verified
Each angle of a rectangle is 90 degrees.

Step by step solution

01

Identify Properties of a Rectangle

Recall that a rectangle is a type of quadrilateral which has opposite sides that are equal and parallel. One of its defining features is that all interior angles are right angles.
02

Define a Right Angle

Understand that a right angle is an angle of exactly 90 degrees. The term 'right angle' is commonly used to describe angles in shapes where they form an L-shape.
03

Apply the Right Angle Definition to a Rectangle

Since a rectangle's defining feature is that all its internal angles are right angles, we can conclude that each angle in a rectangle is 90 degrees.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quadrilateral
A quadrilateral is a polygon with four sides and four vertices. It is one of the basic shapes in geometry. Quadrilaterals can be of many types, based on their side lengths and angles. This category includes shapes such as rectangles, squares, trapezoids, and rhombuses. Each type of quadrilateral has its own unique properties that define its shape and angles.

Characteristics of quadrilaterals include:
  • Having four sides
  • The sum of the interior angles is always 360 degrees
  • The presence of two pairs of opposite sides
Rectangles, for instance, are a special form of quadrilateral because all their angles are right angles, and opposite sides are equal and parallel.
Right Angle
Understanding what a right angle is can help you grasp the structure of many geometric shapes, including rectangles. A right angle is precisely 90 degrees and is signified by the formation of an "L"-shape with two intersecting lines.

Important points about right angles:
  • They occur in various geometric shapes like squares and rectangles.
  • Notably characterized by their perpendicular nature, forming a sharp corner.
  • Indispensable in construction and design, ensuring precision and stability.
The presence of right angles in a rectangle is a defining feature, ensuring that all corners of the shape meet at exact 90-degree angles.
Interior Angles
Interior angles are the angles formed inside a polygon by its sides. In a quadrilateral, like a rectangle or any other four-sided figure, the sum of the interior angles is always 360 degrees. This is a fundamental property of quadrilaterals.

Key points about interior angles:
  • For any quadrilateral, the sum is always 360 degrees.
  • In rectangles, each of the four interior angles is 90 degrees, totaling 360 degrees.
  • The interior angles of a polygon are crucial in calculating other properties like side lengths and area.
Rectangles have a simple arrangement of interior angles, making them an excellent subject of study for beginners learning about geometric shapes.

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Most popular questions from this chapter

\(\overline{\mathrm{AR}}, \overline{\mathrm{AL}},\) and \(\overline{\mathrm{RL}}\) connect points on the sidesof \(\triangle\) TYO. (GRAPH CAN'T COPY) How many midsegments can a triangle have?

Quadrilateral HUGO is a square. Why is HUGO a rhombus?

Tell whether each of the following statements is true or false. A quadrilateral is a parallelogram if it is equilateral.

Tell whether each of the following statements is true or false. A trapezoid can have four equal angles.

Use your ruler to draw each of the following figures. (Draw the diagonals first.) A quadrilateral with equal diagonals that is not a rectangle.
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