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JeanaShupp

Answer:  [tex]\overline{MN}[/tex] and  [tex]\overline{QR}[/tex]


Step-by-step explanation:

Given: In ΔMNO and ΔQRS

[tex]\frac{SQ}{OM}=\frac{SR}{ON}=4[/tex]

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 [tex]\overline{MN}[/tex] and  [tex]\overline{QR}[/tex]

such that [tex]\frac{QR}{MN}=4[/tex]

The other sides are [tex]\;MN{\text{ and }}QR[/tex] 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.

[tex]\begin{aligned}ON \to SR \hfill\\OM \to QS \hfill\\MN \to QR \hfill\\\end{aligned}[/tex]  

Step 2:

The length of [tex]ON[/tex] is 8 units and the length of [tex]SR[/tex] is 32 units.

Therefore, the ratio of [tex]SR[/tex] and [tex]ON[/tex] can be expressed as,

[tex]\begin{aligned}\frac{{SR}}{{ON}} &= \frac{{32}}{8}\\\frac{{SR}}{{ON}}&= 4\\\end{aligned}[/tex]  

Step 3:

The length of [tex]OM[/tex] is 15 units and the length of [tex]SQ[/tex] is 60 units.

Therefore, the ratio of [tex]OM[/tex] and [tex]SQ[/tex] can be expressed as,

[tex]\begin{aligned}\frac{{SQ}}{{OM}}&= \frac{{60}}{{15}}\\\frac{{SQ}}{{OM}}&= 4\\\end{aligned}[/tex]  

Step 4:

The length of [tex]MN[/tex] is 15 units and the length of [tex]QR[/tex] is 60 units.

Therefore, the ratio of [tex]MN[/tex] and [tex]QR[/tex] can be expressed as,

[tex]\begin{aligned}\frac{{QR}}{{MN}}&= \frac{{48}}{{12}}\\\frac{{QR}}{{MN}}&= 4\\\end{aligned}[/tex]  

Step 5:

It can be seen that the ratio of corresponding sides of the triangle are proportional as,

[tex]\Dfrac{{SR}}{{ON}} =\Dfrac{{SQ}}{{OM}} =\Dfrac{{QR}}{{MN}} =4[/tex]  

Therefore, the other sides are [tex]MN[/tex] and [tex]QR[/tex] that satisfies the SSS similarity theorem.

Learn more:  

  1. Learn more about the SAS similarity theorem https://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 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

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