In the accompanying diagram of circle O, chords AB and CD intersect at E. If AE = 3, EB = 4, CE = x, and ED = x + 1, find. CE.
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Answer:
AAS(Angle-Angle-Side) postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent
In triangle RAS and triangle QAT
[Angle]
[Side] [Given]
By Base Angle Theorem states that in an isosceles triangle(i.e, AST), the angles opposite the congruent sides(AS =AT) are congruent.
⇒ [By base ∠'s of isosceles triangle are equal]
By definition of supplementary angles, if two Angles are Supplementary when they add up to 180 degrees.
,
are supplementary and
,
are supplementary.
⇒ and
Two supplementary to equal
Since,
then, we get;
[Angle]
then, by AAS postulates,
By CPCT[Corresponding Part of Congruent Triangles are equal]
Hence Proved!
