Given that the quadrilateral speaker with vertices PEAK is a parallelogram. Find the following. 1.What is the perimeter of the speaker with the given to 4.b and EA= 17? 2.What possible type/s of parallelogram is it?
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Answer:
For any parallelogram the following statements are true: ab = dc ad = bc. The perimeter of a parallelogram is therefore given by: P = 2 (ad + ab)
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Answer:
The shape is a parallelogram. There are different postulates that we can use to determine the answer to each item.
The answers to each item are the following.
\overline{PO}\cong \overline{WE}
PO
≅
WE
\angle O \cong \angle E∠O≅∠E
m\angle W + m\angle E = 180^om∠W+m∠E=180
o
\overline{PR} \cong \overline{RW}
PR
≅
RW
\Delta OPE \cong \Delta OWEΔOPE≅ΔOWE
Quadrilaterals are a closed-figure shape with four sides. There are different kinds of the quadrilateral.
Kinds of Quadrilateral
Rectangle
Square
Rhombus
Parallelogram
Trapezoid
Kite
The given shape is a parallelogram. A parallelogram is a quadrilateral in which opposite sides are parallel. The opposite angles of the parallelogram shown are equal. The opposite sides of the given parallelogram are also equal. But not all the angles are the same.
Explanation to Each Answer
\overline{PO}\cong \overline{WE}
PO
≅
WE
. The line PO and the line WE are opposite sides of the given parallelogram and the opposite sides of the parallelogram are equal.
\angle O \cong \angle E∠O≅∠E . The angles O and E are opposite angles and the opposite angles of a parallelogram are equal.
m\angle W + m\angle E = 180^om∠W+m∠E=180
o
. Angles W and E are adjacent angles and adjacent angles of a parallelogram are supplementary which means that their sum is 180 degrees.
\overline{PR} \cong \overline{RW}
PR
≅
RW
. Line OE is a bisector of line PW, which means that line OE divides line PW into two equal parts. Thus, line PR and RW are equal.
\Delta OPE \cong \Delta OWEΔOPE≅ΔOWE . Line OE is a diagonal of the given parallelogram. This line creates two congruent triangles namely \Delta OPEΔOPE and \Delta OWEΔOWE .
To learn more about quadrilaterals, go to the following websites,
Rectangle: brainly.ph/question/4082839
Sides of a Parallelogram: brainly.ph/question/1893938
Perimeter of a Parallelogram: brainly.ph/question/2774745
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