Answer with Step-by-step explanation:
We are given that a frame ABCD
AB=CD=12 in
BC=DA=35 in
AC=BD=37 in
We know that
In rectangle
Opposite sides are equal.
Diagonals are of equal length.
Each angle is 90 degrees.
Using the property
Opposite sides are equal in given ABCD frame and diagonals are equal in length.
ABCD is a parallelogram.
In triangle ABC
[tex]AB^2+BC^2=(12)^2+(35)^2=1369[/tex]
[tex]AC^2=(37)^2=1369[/tex]
[tex]AC^2=AB^2+BC^2[/tex]
It satisfied Pythagoras theorem. Hence, triangle ABC is a right triangle.
Similarly, triangle BDC is a right triangle.
Angle B=Angle D(Opposite angles are equal in parallelogram)
Angle A=Angle C (Opposite angles are equal in parallelogram)
Angle A=Angle B=Angle C=Angle D=90 degrees
Hence, ABCD is a rectangle.
