In the given figure, ABD = BDC and CD = 4AB. Show that BD = 5BE.
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➡ABD=BDC (given)
➡AEB=DEC (vertically opposite angle)
➡Therefore ∆ABE similar ∆DEC
(AA similarity)
➡therfore, AB/CD=BE/DE---------------1.) [corresponding sides of similar triangles are in proportion]
its given that CD=4AB ➡AB/CD=1/4
Substitute the value of AB/CD=1/4 in equation 1.)
we get,
1/4=BE/DE ➡DE=4BE
➡(BD-BE)=4BE
➡BD=5BE (proved)
➡AEB=DEC (vertically opposite angle)
➡Therefore ∆ABE similar ∆DEC
(AA similarity)
➡therfore, AB/CD=BE/DE---------------1.) [corresponding sides of similar triangles are in proportion]
its given that CD=4AB ➡AB/CD=1/4
Substitute the value of AB/CD=1/4 in equation 1.)
we get,
1/4=BE/DE ➡DE=4BE
➡(BD-BE)=4BE
➡BD=5BE (proved)
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