Pls ans this quickly
Answers
a)
In triangle AEC, AE = 10 cm, CE = 8cm, Angle C = 90 degress
Using pythagoras theorem,
(AE)^2 = (AC)^2 + (AE)^2
100 - 64 = (AC)^2
AC = 6 cm = BC ( C is midpoint of AB, so AC = CB )
b)
In triangle ACE and BCE
AC = BC ( c is midpoint )
EC = EC ( common side )
angle ECA = angle ECB ( 90 degrees)
Therefore, triangle ACE is congruent to triangle BCE ( by SAS congruent critrion)
So, AE = BE ( congruent parts of congruent triangles are equal )
Ratio of AE and BE, AE:BE = 1:1
c)
As AE = BE, AEB is an isosceles triangle
d)
CE is the altitude as well as median of triangle AEB
e)
As EC is median, it divides triangle AEB into 2 equal areas, area of BCE is half of ABE
so ratio of ABE and BCE = 2:1
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