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Use similar triangles to find side lengths. In the diagrams below, A ABC is similar toARST. Use a proportion with sides AB and RS tofind the scale factor of ABC to RST. Use the scale factor from Part I and a proportion to find the length of ST. Use the scale factor from Part I and a proportion to find the length of RT.

Use Similar Triangles To Find Side Lengths In The Diagrams Below A ABC Is Similar ToARST Use A Proportion With Sides AB And RS Tofind The Scale Factor Of ABC To class=

Sagot :

When we have similar triangles, we can say that all of the corresponding sides of each of the triangles are in proportion. Then we can say that:

[tex]\frac{AB}{RS}=\frac{AC}{RT}=\frac{BC}{ST}[/tex]

Since we have that the measure of sides AB and RS, we can obtain the ratio between these sides - which is, at the same time, the scale factor of triangle ABC to triangle RST:

[tex]\begin{gathered} AB=18 \\ RS=6 \\ \frac{AB}{RS}=\frac{18}{6}=3 \end{gathered}[/tex]

Therefore, the sides of the triangle ABC are 3 times greater than the sides of the triangle RST.

In summary, therefore, we can say that the scale factor of ∆ABC to ∆RST is 3. In other words, ∆ABC is 3 times greater than ∆RST, or we can say that we need to multiply the sides of ∆RST by 3 to obtain the sides of ∆ABC.

[We can also say that we need to multiply the sides of ∆ABC by 1/3 to obtain the sides of ∆RST.]

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