altitude Sum solve IT step by step
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Answer:
DC = BD
Step-by-step explanation:
Draw the triangle Right Angled at 'B'.
Drop a perpendicular from B to AC to meet at C
Now, consider the triangles: ABC and ADB
<ABC = 90 = <ADB
<BAC = <DAB (common angle)
By AA criterion ABC and ADB are similar triangles
AB/AD = BC/DB = AC/AB
AB/AD = BC/AD .. [BD=AD given]
Hence, AB=BC
Similarly, ABC and CDB can be proved similar
<ABC = 90 = <CDB
<BCA = <DCB
By AA criterion
AB/CD = BC/DB = AC/CB
AB/CD = BC/DB
AB/CD = AB/DB [AB=BC]
1/CD = 1/DB
DC = BD
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