The other sides are \(\;MN{\text{ and }}QR\) that satisfies the SSS similarity theorem.
Further explanation:
SSS similarity theorem states that the three sides of one triangle is proportional to the corresponding sides of the another triangle.
Step by step explanation:
Step 1:
From the given figure it can be observed that the corresponding sides are written below.
\(\begin{aligned}ON \to SR \hfill\\OM \to QS \hfill\\MN \to QR \hfill\\\end{aligned}\)
Step 2:
The length of \(ON\) is 8 units and the length of \(SR\) is 32 units.
Therefore, the ratio of \(SR\) and \(ON\) can be expressed as,
\(\begin{aligned}\frac{{SR}}{{ON}} &= \frac{{32}}{8}\\\frac{{SR}}{{ON}}&= 4\\\end{aligned}\)
Step 3:
The length of \(OM\) is 15 units and the length of \(SQ\) is 60 units.
Therefore, the ratio of \(OM\) and \(SQ\) can be expressed as,
\(\begin{aligned}\frac{{SQ}}{{OM}}&= \frac{{60}}{{15}}\\\frac{{SQ}}{{OM}}&= 4\\\end{aligned}\)
Step 4:
The length of \(MN\) is 15 units and the length of \(QR\) is 60 units.
Therefore, the ratio of \(MN\) and \(QR\) can be expressed as,
\(\begin{aligned}\frac{{QR}}{{MN}}&= \frac{{48}}{{12}}\\\frac{{QR}}{{MN}}&= 4\\\end{aligned}\)
Step 5:
It can be seen that the ratio of corresponding sides of the triangle are proportional as,
\(\Dfrac{{SR}}{{ON}} =\Dfrac{{SQ}}{{OM}} =\Dfrac{{QR}}{{MN}} =4\)
Therefore, the other sides are \(MN\) and \(QR\) that satisfies the SSS similarity theorem.
Learn more:
- Learn more about the SAS similarity theorem https://brainly.com/question/3318919
- Learn more about the pythagorean theorem used in the right angle trianglehttps://brainly.com/question/10462263
- Learn more about midpoint of the segment https://brainly.com/question/3269852
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Triangle similarity.
Keywords: Triangle, similarity, sides, proportional, ratio, length, theorem, diagram, corresponding sides, angles, sum, fraction
