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2x+3 = 3x-2 [sides opposite to equal angles]
x = 5
Equal sides = 13
Using Pythagoras theorem we get, base of each half-triangle = 5
Using the property that the perpendicular to the base of an isosceles triangle bisects the base: , we get the base = 10
Area = ½ x Base x Height = ½ x 10 x 12 = 60
In the figure above, If ABCD is a square and AE = EB, then which of the following statements is NOT true?
Select all that apply.
Answer: D, E
Using Pythagoras theorem:
In ∆AED AE2 + AD2 = DE2
In ∆BEC BE2 + BC2 = CE2
But AD = BC [sides of a square] and AE = BE [Given]
So DE = CE A is TRUE
DE = CE so the angles opposite must also be equal p = t B is TRUE
q=90-p and s = 90 – t so q = s C is TRUE
r = s if BE = BC but BE = ½ BC. D is FALSE
We know in a 30-60-90 triangle, if r = 30 then BE = √3BC but BE = ½ BC. E is FALSE.
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