Answer:
Given: It is given that and .
To Prove: ABCD is a parallelogram.
Statements
1. and
Reason: Given
2. are alternate interior angles
Reason: Def of alternate interior angles
3.
Reason: Alternate interior angles are congruent
4.
Reason: Reflexive property
5.
Reason: SAS congruency theorem
6.
Reason: Corresponding Parts of Congruent triangles are Congruent (CPCTC)
7. ABCD is a parallelogram
Reason: Parallelogram Side Theorem
Step-by-step explanation:
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Step-by-step explanation:
5(tanx)^2 -2 +tanx=0
let tanx=y
5y^2 + y-2=0
y=0.5403 or y= -0.7403
tanx=0.5403
x=arctan(0.5403)
x=28.38°
or
tanx=-0.7403
x=arctan(-0.7403)
x=143.49°
Distance Formula: 
Apply the points: 
Solve: 
Since the square root of 218 cannot be simplified, the answer is

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