Open in App
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Chapter 30: Chapter 30

Problem 577

Next question

Construct the perpendicular bisector of a given segment. Bisect a given angle.

Short Answer

Expert verified
To construct the perpendicular bisector of a given segment AB, draw intersecting arcs above and below the segment when the compass is placed on points A and B. Then, join the intersecting points with a straightedge. To bisect a given angle ∠XYZ, draw arcs that intersect angle sides from the vertex, draw intersecting arcs from the new points, and draw a ray from the vertex through the intersection of these arcs. This ray is the angle bisector.
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Try Premium for free

Over 22 million students worldwide already upgrade their learning with Vaia!

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Construct the perpendicular bisector of a given segment.

To begin, let's name the given segment as AB. We will follow these steps to construct the perpendicular bisector: 1. Place the compass needle on point A and open it to slightly more than half the length of the segment AB. Draw an arc above and below the segment. 2. Without changing the compass opening, place the needle on point B and draw an arc intersecting the previous arcs above and below the segment. 3. Use a straightedge to join the points where the arcs intersect above and below the segment. This line is the perpendicular bisector of segment AB.

Step 2: Bisect a given angle.

Let's assume we have an angle ∠XYZ that needs to be bisected. Here are the steps to construct the angle bisector: 1. Place the compass needle on the vertex of the angle (point Y) and draw an arc such that it intersects both rays XY and YZ, creating two new points P and Q, respectively. 2. Now, place the compass needle on point P, and draw an arc in the interior of the angle (choose an opening that will allow the arc to be visible). 3. Without changing the compass opening, place the compass needle on point Q and draw another arc intersecting the previous arc you drew in step 2. 4. Use a straightedge to join point Y (vertex) with the point where the two arcs intersect in the interior of the angle ∠XYZ. This newly drawn ray is the angle bisector of ∠XYZ. Now, you have the knowledge to construct both the perpendicular bisector of a segment and bisect a given angle using a compass and a straightedge.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 30

Construct the segment of length equal to \(\mathrm{a} \cdot \mathrm{b}\) where a and \(\mathrm{b}\) are the lengths of the segments below. (Unit length is shown below.)
Chapter 30

Construct the mean proportional between two given segments.
Chapter 30

Construct a line perpendicular to a given line through a given point on the given line.
Chapter 30

Divide a given line segment into parts proportional to given line segments.
Chapter 30

Divide any segment into three congruent segments.
See all solutions

More chapters from the book ‘Geometry’

See all chapters

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App
Create your free account now
Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Math

Probability and Statistics

Read Explanation
Math

Decision Maths

Read Explanation
Math

Mechanics Maths

Read Explanation
Math

Geometry

Read Explanation
Math

Pure Maths

Read Explanation
Math

Statistics

Read Explanation
View all explanations