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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';
What is the simplified version of a times b times c?
The product can be expressed as abc.
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
What are the lengths of the diagonals of the quadrilateral abcd when ab is 4.3 cm bc is 3.4 cm cd is 3.8 cm angle abc is 95 degrees and angle bcd is 115 degrees?
If you mean quadrilateral ABCD then by using the cosine rule diagonal AC equals 5.71 cm and diagonal BD equals 6.08 cm both rounded to two decimal places.
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.
