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Abcd is a parallelogram ab equals bc and angle abc equals 90 degree explain why abcd is a square?
Opposite sides of a parallelogram are equal. So ab = dc and ad = bc. But you are also told that ab = bc. So all four sides are equal. Opposite angles of a parallelogram are equal. So abc =90 degrees implies that cda is 90 degrees. The remaining two angles add up to 360 - (abc + cda) = 180 degrees and both are equal. So they, too , must be 90 degrees each. So all four angles are equal. A parallelogram with four equal sides and four equal angles is called a square.
If one pair of sides of a quadrilateral is parallel and congruent then the quadrilateral is a parallelogram?
== == yes. suppose the quad ABCD has AB and CD equal and parallel. Then the triangles ABC and CDA are congruent by SAS axiom; so the quad is a parallelogram
A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel prove?
A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel Let ABCD be a quadrilateral in which ABCD and AB=CD, where means parallel to. Construct line AC and create triangles ABC and ADC. Now, in triangles ABC and ADC, AB=CD (given) AC = AC (common side) Angle BAC=Angle ACD (corresponding parts of corresponding triangles or CPCTC) Triangle ABC is congruent to triangle CDA by Side Angle Side Angle BCA =Angle DAC by CPCTC And since these are alternate angles, ADBC. Thus in the quadrilateral ABCD, ABCD and ADBC. We conclude ABCD is a parallelogram. var content_characters_counter = '1032';
Why are the opposite sides of a parallelogram equal?
It is difficult to give a proof without diagrams, but here goes: Suppose you have the parallelogram with ABDC and ADBC Then angle ABC = angle CDA. Now draw the diagonal AC. Then angle ACB = angle CAD (alternate angles). So, in triangles ABC and ACD, two pairs of angles are equal so that all three pairs are equal (in each triangle the three add to 180 deg). and AC is a common side. So the two triangles are congruent and so AB = DC and AD = BC
What is the sum of ABC?
The answer depends on what ABC is!
