Match the following reasons with the statement givem

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!

there are no short passages to look at

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0