The figure below shows rectangle ABCD: Rectangle ABCD with diagonals AC and BD passing through point E

The following two-column proof with missing statement proves that the diagonals of the rectangle bisect each other:

Statement Reason
ABCD is a rectangle. Given
Line segment AB and Line segment CD are parallel Definition of a Parallelogram
Line segment AD and Line segment BC are parallel Definition of a Parallelogram
Alternate interior angles theorem
Line segment BC is congruent to line segment AD Definition of a Parallelogram
∠ ADB ≅∠ CBD Alternate interior angles theorem
ΔADE ≅ ΔCBE Angle-Side-Angle (ASA) Postulate
Line segment BE is congruent to line segment DE CPCTC
Line segment AE is congruent to line segment CE CPCTC
Line segment AC bisects Line segment BD Definition of a bisector
Which statement can be used to fill in the blank space? (5 points)

∠ ABD ≅∠ DBC
∠ CAD ≅∠ ACB
∠ BDA ≅∠ BDC
∠ CAB ≅∠ ACB

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step-by-step explanation:

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the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

rotation point l

step-by-step explanation: