In the diagram, StartFraction S Q Over O M EndFraction = StartFraction S R Over O N EndFraction = 4.
2 answers:
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:
- AAA similarity : two triangles are similar if all three angles in the first triangle equal the corresponding angle in the second triangle
- AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles are similar.
- SSS similarity : If the corresponding sides of the two triangles are proportional, then the two triangles are similar.
- 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
∴
∵ SR = 32
∵ ON = 8
- Find the ratio of SR and ON
∴
∵ MN = 12 units
∵ QR = 48
- Find the ratio between QR and MN
∴
- The ratio between the corresponding sides are equal
∴
- 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
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