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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q10CE. (page 155)

10. Given: $\overset{鈫�}{N O}$ bisects $鈭� N$ .What can you conclude from each of the following additional statements?
a. $P$ lies on $\overset{鈫�}{N O}$
b. The distance from a point $Q$ to each side of $鈭� N$ is 13.

Short Answer

Expert verified

a. $P$ is equidistance from each side of $鈭� N$
b. lies on $\overset{鈫�}{N O}$

Step by step solution

01

Part a. Step 1. The meaning of P lies on NO→

$P$ lies on role="math" localid="1649151298117" $\overset{鈫�}{N O}$ means a point on $\overset{鈫�}{N O}$ is named as $鈭� N$

02

Part a. Step 2. Show that NO→ is equidistance from each side of ∠N

When a line divides an angle into two congruent angles then it is equidistance from each side of that angle

So, $\overset{鈫�}{N O}$ is equidistance from each side of $鈭� N$

03

Part a. Step 3. Show that P is equidistance from each side of ∠N

As $P$ lies on $\overset{鈫�}{N O}$

Thus, $P$ is equidistance from each side of $鈭� N$

04

Part b. Step 1. Meaning of “distance from a point Q to each side of ∠N is 13”

$Q$ is equidistance from each side of $鈭� N$

05

Part b. Step 2. Show that line from Q bisect ∠N

When a line is an equidistance from each side of that angle then it divides an angle into two congruent angles

So, a line from $Q$ bisects $鈭� N$

06

Part b. Step 3. Show that Q lies on

As $Q$ and $\overset{鈫�}{N O}$ both bisects $鈭� N$

Thus, $Q$ lies on $\overset{鈫�}{N O}$

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Most popular questions from this chapter

For the following figure, do the SAS postulates justify that the two triangles are congruent?

The pentagons shown are congruent. Complete.

If $\overset{炉}{CA} 鈯� \overset{炉}{LA},$ name two right angles in the figures.

Plot the given points on graph paper. Draw $螖 ABC$ and $螖 DEF$ . Copy and complete the statement $螖 ABC 鈮� \underset{炉}{?}$ .

$A (鈭� 7, 鈭� 3)$ $B (鈭� 2, 鈭� 3)$ $C (鈭� 2, 0)$

$D (0, 1)$ $E (5, 1)$ $F (0, 鈭� 2)$

Suppose that $螖 B I G 鈮� 螖 C A T$ , then complete the following statement.

$B I =__$

For the following figure, can the triangle be proved congruent. If so, what postulate can be used?

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