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Ivenika [448]
2 years ago
14

Can the triangles below be proven similar?

Mathematics
1 answer:
jeka942 years ago
3 0

\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}

<u>Yes </u><u>!</u><u> </u><u>they </u><u>ofcourse</u><u> </u><u>are </u><u>similar</u><u> </u><u>and </u><u>here </u><u>goes </u><u>the </u><u>explanation</u><u> </u><u>behind </u><u>that </u><u>~</u>

two triangles are said to be similar by SAS postulate in case the ratios of their side lengths comes out to be equal along with one angle lying in between the side lengths

<u>in </u><u>this </u><u>case </u><u>,</u>

\frac{AB}{BD}  \: should \: be \: equal \: to \:  \frac{EB}{BC} \\

so , let's check if the ratio is equal or no ~

\implies\frac{AB}{BD}  =  \frac{27}{18}  =  \frac{3}{2}  \\  \\ \implies \:  \frac{EB}{BC}  =  \frac{36}{24}  =  \frac{3}{2}  \\  \\ \therefore \:  \frac{AB}{BD}  =  \frac{EB}{BC}

Also ,

∠ABE = ∠CBD

<u>since </u><u>they </u><u>both </u><u>are </u><u>vertically</u><u> </u><u>opposite </u><u>,</u><u> </u><u>i.</u><u>e</u><u>.</u><u> </u><u>,</u><u> </u><u>angles </u><u>with </u><u>the </u><u>same </u><u>vertex </u><u>B </u><u>.</u>

thus the triangles are similar by SAS postulate !

hence , <u>Option </u><u>A</u> is correct !

hope helpful ~

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