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Chapter 8: Problem 4

In trapezoid QRST, name the bases, the legs, and the base angles.

Short Answer

Expert verified
Bases: QR and ST; Legs: QS and RT; Base angles: 鈭燪, 鈭燫, 鈭燬, and 鈭燭.

Step by step solution

01

Identify the Trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides. In trapezoid QRST, we need to first identify all its sides.
02

Identify the Bases

In a trapezoid, the parallel sides are called the bases. Examine trapezoid QRST to find which pairs of sides are parallel to each other. Let's assume that sides QR and ST are parallel; therefore, they are the bases.
03

Identify the Legs

The non-parallel sides in a trapezoid are called the legs. After identifying the bases QR and ST, the remaining sides QS and RT must be the legs.
04

Identify the Base Angles

Base angles in a trapezoid are pairs of angles adjacent to each of the bases. For base QR, the base angles are 鈭燪 and 鈭燫. For base ST, the base angles are 鈭燬 and 鈭燭.

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Key Concepts

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

Trapezoid
A trapezoid is a fundamental shape in geometry that falls under the category of quadrilaterals. It is defined specifically as a four-sided shape that has at least one pair of parallel sides. These parallel sides distinguish a trapezoid from other quadrilaterals like rectangles, squares, and rhombuses. There are different types of trapezoids including the isosceles trapezoid where the non-parallel sides, called the legs, are of equal length. Trapezoids find their importance in various real-world applications such as architecture and design.
Quadrilateral
Quadrilaterals are polygons that have four sides and four angles. Trapezoids are just one type of quadrilateral, alongside others like squares, rectangles, and parallelograms. What makes quadrilaterals interesting is the variety of forms they can take, due to different arrangements and lengths of sides and angles. The sum of all internal angles in any quadrilateral is always 360 degrees. This property helps in solving various geometric problems and in determining unknown angles when the other angles are known.
Parallel Sides
The concept of parallel sides in geometry is crucial in defining and differentiating various shapes, particularly trapezoids. Two lines or sides are said to be parallel if they lie in the same plane and never intersect, no matter how far they are extended. In the specific context of trapezoids, the presence of at least one pair of parallel sides (the bases) is the defining characteristic. Parallel lines have the same slope if visualized on a coordinate plane. This quality can be used to prove that two sides are parallel when solving geometric problems.
Base Angles
In trapezoids, base angles refer to the angles that are adjacent to the parallel sides, or bases of the trapezoid. Each pair of parallel sides has a pair of base angles associated with them. Understanding base angles is important because if a trapezoid is isosceles, the base angles are equal. These angles help in various calculations and proofs within geometry, like when determining properties of the trapezoid or when trying to solve for unknown angles non-directly based on given information about other angles and sides.

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Most popular questions from this chapter

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Determine whether it is possible for a trapezoid to have the following conditions. Write yes or no. If yes, draw the trapezoid. one leg longer than either base

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