Question

To prove that the triangles are similar by the SSS similarity theorem, which other sides or angles should be used?]

Answer 1

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:  

1. Learn more about the SAS similarity theorem brainly.com/question/3318919
2. Learn more about the pythagorean theorem used in the right angle trianglehttps://brainly.com/question/10462263
3. Learn more about midpoint of the segment 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

Answer 2

Answer:  $\overline{MN}$ and  $\overline{QR}$

Step-by-step explanation:

Given: In ΔMNO and ΔQRS

$\frac{SQ}{OM}=\frac{SR}{ON}=4$

To prove that the triangles are similar by the SSS similarity theorem  [corresponding sides of similar triangles are proportional], there must be the third pair of corresponding sides,

That must be $\overline{MN}$ and  $\overline{QR}$

such that $\frac{QR}{MN}=4$