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Question 8 (5 points)
When constructing an angle bisector of an angle, the first step is to draw:
A. a segment bisector of both the sides of the angle.
B. a line passing through the intersection of the arcs and the vertex.
C. two arcs in the interior of the angle.
D. an arc using the vertex as the center, intersecting both sides of the angle.

Question 9 (5 points)
Three points, Q, R, and S, lie on the same line such that R lies between Q and S. Find QS if RS = 19 and QR = 32.



Answer :

GinnyAnswer
Alright, let's break down this problem step by step.

Question 9:
We are given three points [tex]\( Q \)[/tex], [tex]\( R \)[/tex], and [tex]\( S \)[/tex] which lie on the same line. Further, we know that [tex]\( R \)[/tex] is between [tex]\( Q \)[/tex] and [tex]\( S \)[/tex], and we are given the distances:

1. [tex]\( RS = 19 \)[/tex]
2. [tex]\( QR = 32 \)[/tex]

We need to find the distance [tex]\( QS \)[/tex].

Since [tex]\( R \)[/tex] lies between [tex]\( Q \)[/tex] and [tex]\( S \)[/tex], the total distance [tex]\( QS \)[/tex] can be found by adding the distances [tex]\( QR \)[/tex] and [tex]\( RS \)[/tex]:

[tex]\[ QS = QR + RS \][/tex]

Plugging in the given values:

[tex]\[ QS = 32 + 19 \][/tex]

So,

[tex]\[ QS = 51 \][/tex]

Therefore, the distance [tex]\( QS \)[/tex] is [tex]\( 51 \)[/tex].

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