Me! provide statements and reasons for the proof of the triangle angle bisector theorem. given: line bd bisects ∠abc. auxiliary line ea is drawn such that line ae line bd | |. auxiliary line be is an extension of line bc. prove: ad/dc = ab/bc

Refer to the attached image.

Given: Line BD bisects ∠ABC.

Construction: Auxiliary Line EA is drawn such that Line AE is parallel to Line BD . Auxiliary Line BE is an extension of Line BC.

To prove:

Proof:

Since Lines EA and BD are parallel,

(Corresponding angles)

So, (Alternate angles)

(because it is given that BD bisects ∠ABC )

So, by the above three equations, we get

So, BE=AB (Opposite sides equal to opposite angles are equal) (Equation 1)

Now, consider triangle ACE,

Since AE is parallel to BD.

By Basic Proportionality theorem, which states

" If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio."

So,we get

By using equation 1, we get

Hence, proved.

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.

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