Question

In the diagram, StartFraction S Q Over O M EndFraction = StartFraction S R Over O N EndFraction = 4.

Answer 1

Answer:

MN and QR should be used to prove that the triangles are similar by the SSS similarity theorem ⇒ 2nd answer

Step-by-step explanation:

Let us revise the cases of similarity:

1. AAA similarity : two triangles are similar if all three angles in the first  triangle equal the corresponding angle in the second triangle
2. AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles  are similar.  
3. SSS similarity : If the corresponding sides of the two triangles are  proportional, then the two triangles are similar.  
4. SAS similarity : In two triangles, if two sets of corresponding sides  are proportional and the included angles are equal then the two  triangles are similar.  

In Δs MNO and QRS

∵ SQ = 60

∵ OM = 15

- Find the ratio between SQ and OM

∴ $\frac{SQ}{OM}=\frac{60}{15}=4$

∵ SR = 32

∵ ON = 8

- Find the ratio of SR and ON

∴  $\frac{SR}{ON}=\frac{32}{8}=4$

∵ MN = 12 units

∵ QR = 48

- Find the ratio between QR and MN

∴ $\frac{QR}{MN}=\frac{48}{12}=4$

- The ratio between the corresponding sides are equal

∴ $\frac{SQ}{OM}=\frac{SR}{ON}=\frac{QR}{MN}= 4$

- By using the third case of similarity SSS

∴ Δ MNO is similar to Δ QRS by SSS similarity theorem

∴ You should use sides MN and QR

Answer 2

Answer:

B

Step-by-step explanation:

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