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91Ó°ÊÓ

For the following symbols, find the symbols that represent a line, segment, ray, or length.

a. PQ¯

b. PQ→

c. PQ↔

d. PQ

Short Answer

Expert verified

a.The symbolPQ¯ represents a segment.

b.The symbol PQ→represents a ray.

c. The symbol PQ↔ represents a line.

d. The symbol PQ represents the length of the segment PQ¯.

Step by step solution

01

Part a. Step 1. Define the concept.

A segment is part of the line connecting two points. These two points are the endpoints of the segment.

02

Part a. Step 2. Find the symbol PQ¯ that represents a line, segment, ray, or length.

The symbol PQ¯consists of two endpoints Pand Q, also all the points between Pand Q.

Since the symbol PQ¯has two endpoints, thus the symbol PQ¯ represents a segment.

03

Part a. Step 3. Graphical interpretation of segment.

The following figure represents a segment PQ¯.

04

Part b. Step 1. Define the concept.

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.

05

Part b. Step 2. Find the symbol PQ→ that represents a line, segment, ray, or length.

The symbol PQ→consists of one endpoint PandQgoes on infinitely.

Since the symbol PQ→has one endpoint, thus the symbol PQ→ represents a ray.

06

Part b. Step 3. Graphical interpretation of ray.

The following figure represents a segment PQ→.

07

Part c. Step 1. Define the concept.

A line goes in the infinite direction on both sides, thus a line has no endpoints.

08

Part c. Step 2. Find the symbol PQ↔ that represents a line, segment, ray, or length.

The symbol PQ↔consists of no endpoints.

Since the symbolPQ↔ has no endpoints, thus the symbol PQ↔ represents a ray

09

Part c. Step 3. Graphical interpretation of segment.

The following figure represents a line PQ↔.

10

Part d. Step 1. Define the concept.

The length of a line segment can be measured by finding the distance between its two endpoints. It is the path between the two points with a definite length that can be measured.

11

Part d. Step 2. Find the symbol PQ that represents a line, segment, ray, or length.

Here the symbol PQrepresents the distance between the two endpointsPandwidth="14">Qwhich is the length of the segment.

12

Part d. Step 3. Step description.

Thus, the symbolPQ represents the length of the segment PQ¯ .

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