Question

1. in the figure, the horizontal lines are all parallel to one another. ( ab = bc = cd ). find ( jm ).

a. 4
b. 8
c. 12
d. 16

1. given: ( \frac { x } { 5 } + 6 = 9 )

prove: ( x = 15 )
match each statement to the correct reason.
( \frac { x } { 5 } + 6 = 9 )
( \frac { x } { 5 } = 3 )
( x = 15 )
choices
multiplication property of equality
given
subtraction property of equality
addition property of equality
division property of equality

Explanation:

Question 13

Step1: Apply the theorem of parallel lines

When three or more parallel lines cut off equal segments on one transversal, they cut off equal segments on any other transversal. Here, since \(AB = BC=CD\), then \(JL = LK = KM\).

Step2: Calculate \(JM\)

Given \(ML = 4\), and \(JM=JL + LK+KM\). Since \(JL = LK = KM = 4\), then \(JM=4\times3\).

• For the equation \(\frac{x}{5}+6 = 9\), this is the starting equation, so the reason is "Given".
• To get from \(\frac{x}{5}+6 = 9\) to \(\frac{x}{5}=3\), we subtract 6 from both sides of the equation. According to the subtraction property of equality: if \(a + b=c\), then \(a=c - b\). So the reason is "Subtraction Property of Equality".
• To get from \(\frac{x}{5}=3\) to \(x = 15\), we multiply both sides of the equation by 5. According to the multiplication property of equality: if \(\frac{a}{b}=c\), then \(a = b\times c\) (\(b

eq0\)). So the reason is "Multiplication Property of Equality".

Answer:

C. 12

Question 14