Question

TEXT ANSWER

Question 7
Are the sides proportional?
Set up each ratio of sides and determine if they are equal ratios. Show all of your work.
3.61 cm
R
44°
11.97 cm
9.71 cm
N
T
17.955 cm
14.565 cm
121°
M
44°
5.415 cm

Answer 1

Yes.

Explanation:

We need to make sure that we match up the right sides before checking for proportionality.

From the picture, we can see that SRT pairs with MLN.

It's easier to see if you draw a diagram of MLN on paper with the same orientation as SRT.

Were you to do this, you would see that as SR lies on the left side of SRT, so does MLN lie on the left side of ML.

Also, both ST of SRT and MN of MLN lie on the right side and RT of SRT and LN of MLN are the base.

Thus, the proportions are

`(SR)/(ML)=(ST)/(MN)=(RT)/(LN) \\\\\\(3.61)/(5.415)=(2)/(3) \\\\(9.71)/(14.564)=(2)/(3)\\ \\ (11.97)/(17.955)=(2)/(3)`

Since all the ratios simplify to 2/3 and are equal, the sides are proportional.