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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!
If ABCD is a parallelogram and the two diagonals are equal find the measure of angle ABC?
90 degrees - the parallelogram is a rectangle (or a square) if the diagonals are equal.
In this parallelogram bad is supplementary to?
<ABC
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.
The parallelogram ABCD is a rhombus what type of triangle is ABC?
isosceles triangle
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 s the process of trihybrid cross?
In a trihybrid cross, three traits are considered. To perform the cross, the genotypes of the parents for all three traits must be determined. Then, the Punnett square or probability analysis is used to predict the genotypes and phenotypes of the offspring based on the inheritance patterns of the three traits.
Right triangle ABC could also be an isosceles triangl?
Yes if it's 90, 45 and 45 degrees
In a parallelogram show that bisectors of adjacent angles intersect at right angles?
Label the parallelogram ABCD (with AB parallel to DC, AD parallel to BC) and the point where the angle bisectors of DAB and ABC meet X. It is needed to be shown that angle AXB is 90o.Call angle DAB a and angle ABC b. Then the bisectors of these angles are 1/2a and 1/2b.First note that for a parallelogram, opposite angles are equal, ie:ADC = ABC = aDAB = DCB = bAlso, the sum of all angles in a quadrilateral (and a parallelogram is one) in 360o. Thus:360o = DAB + ABC + BCD + CDA360o = a +b + a + b360o = 2a +2bOr dividing by 2:180o = a + band again by 2:90o = 1/2a + 1/2b - [1]Now consider triangle AXB. Angle XAB = 1/2b, XBA = 1/2b. So angle:AXB = 180o - (XAB + XBA)AXB = 180o - (1/2a + 1/2b)AXB = 180o - 90o (As shown in [1] above)AXB = 90oThus the bisectors of adjacent angles of a parallelogram meet at right angles.Opposite angles of a parallelogram can be shown to be equal by extending sides AB and DC and then using corresponding and alternate angles.Alternatively, adjacent angles of a parallelogram can also be shown to sum to 180o by extending line AB (to any point Y beyond B) and using that DAY and CBY are corresponding angles and that ABC and CBY sum to 180o since ABY is a straight line.
A mount shaped like a parallelogram is used for binoculars so people of different heights can view an object without having to reposition the angle of the binoculars?
ABC
Why can't Kingaroy have its own ABC Shop?
Exactly The ABC Australia could Buy the Ladies Fashion Boutique in Kingaroy for $225,000.00 and Rename the Building ABC Shop with the ABC Australia Logo and they could put lots of ABC Tv Australia Merchandise from Different Shows onto the Shelfs in the Store.
Where can one find ABC News in AU?
There are many places where one could find ABC News in Australia. One could view ABC News online at their official website from this location and many other locations in the world.
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';
