In triangle ABC AB = 15 cm, AC = 10 cm, AD is the bisector A. From point D a straight line is drawn parallel
| September 24, 2021 | education
In triangle ABC AB = 15 cm, AC = 10 cm, AD is the bisector A. From point D a straight line is drawn parallel to AB until it intersects with AC at point E. Find AE, EC, DE.
DE || AB, ΔСDE is similar to ABC, then DE / CE = AB / AC = 15/10 = 1.5
angle BAD = angle ADE (parallel straight lines are cut by straight line AD)
angle ADE = angle DAE (AD bisector)
ΔАDE is isosceles, АЕ = DE, we will compose the system
DE / CE = 1.5
DE + CE = 10, because (AE + CE = 10), we solve
1.5 * CE + CE = 10
CE = 4
AE = DE = 6
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