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Q: If ABCD is a parallelogram in which AB is parallel to CD prove that angle A equals angle B?

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There are 5 ways to prove a Quadrilateral is a Parallelogram. -Prove both pairs of opposite sides congruent -Prove both pairs of opposite sides parallel -Prove one pair of opposite sides both congruent and parallel -Prove both pairs of opposite angles are congruent -Prove that the diagonals bisect each other

If two opposite sides are congruent in length and direction then they are parallel sides. THat would mean the other two sides are congruent making 4 parallel sides or a parallelogram

Corresponding angle are used to prove if lines are parallel. If they are congruent then the lines cut by the transferal are parallel.

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';

Yes, a rectangle is a special kind of parallelogram - one that has a right angle. (You can prove that if it has one right angle all angles are right.)

Yes, that is what is rectangle is. One can prove that all of the angles are right angles.

Opposite angles of quadrilaterals in general can vary over quite a range of degrees. In order for a quadrilateral to be a parallelogram, two sets of parallel lines intersect. Imagine a parallelogram resting on its base. Focus on one of the base interior angles. Now flip the parallelogram so that its top is now the base. The shapes will be completely congruent, both in angle size and lengths of sides. Parallelogram is simply a special class of quadrilateral, and this property is part of how parallelograms are defined. Alternative Answer: It is rather difficult to prove a geometric proposition while working within the limitations of this browser! But here goes: Call the parallelogram is ABCD with AB parallel to DC horizontal, and AD parallel to BC. Consider AD and BC which are parallel, with transversal DC. Then the interior angles on the same side are supplementary. That is, angles ADC and DCB are supplementary. Now consider AB and DC which are parallel, with transversal AD. Then the interior anlges on the same side are supplementary. That is, angles BAD and ADC are supplementary. So in the above two paragraphs we have shown that angles ADC + DCB = BAD + ADC therefore angle DCB = angle BAD [subtracting angle ADC from both sides] that is, one pair of opposite angles are equal. You can prove the other pair is equal either by the fact that they are supplementary to these, or by the symmetry of the argument.

Angle a plus angle b subtract from 180 equals angle c

you can prove any one of these statements to prove that quadrilateral is a rectangle: -- Opposite sides are parallel and any one angle is a right angle. -- Opposite sides are equal and any one angle is a right angle. -- All four angles are right angles. -- Adjacent angles are complementary, and one of them is a right angle. -- Opposite sides are either equal or parallel, and area is equal to the product of two adjacent sides. -- Diagonals are equal.

You can show that two lines cut by a transversal are parallel in a number of ways. (1) Show that the consecutive interior angles are supplementary. Let's say your lines are arranged like this (ignore the periods, they're just there so the spacing is right): ......................1 | 2 --------------------|----------------------- .......................8| 3 .........................| ......................7 | 4 --------------------|----------------------- ......................6 | 5 If the lines are parallel, the measures of all the consecutive interior angles should be supplementary. The following should be true: Angle 8 + Angle 3 = 180 degrees Angle 3 + Angle 4 = 180 degrees Angle 4 + Angle 7 = 180 degrees and Angle 7 + Angle 8 = 180 degrees (2) You can also prove that the lines are parallel by showing that the corresponding angles are congruent. Using the line arrangement above, prove any of the following to be true: Angle 1 = Angle 7 Angle 2 = Angle 4 Angle 3 = Angle 5 or Angle 8 = Angle 6 (3) Finally, you can use alternate angles (either interior or exterior). To use alternate interior angles, prove that: Angle 3 = Angle 7 or Angle 4 = Angle 8 To use alternate exterior angles, prove that: Angle 1 = Angle 5 or Angle 2 = Angle 6 Well, there you have it! Best of luck!

A quadrilateral, in general, is not a parallelogram. If it is a parallelogram then you will have some additional information about its sides and angles. If you do not have such information it is not possible to prove that it is a parallelogram. Draw a diagonal which will divide the quadrilateral into two triangles and use the additional information that you have to show that the triangles are congruent. This can then be used to show equality of sides or of angles: the latter can then be used to show that sides are parallel. Note that the choice of which diagonal may influence how (if at all) you proceed.

Suppose that the parallelogram is a rhombus (a parallelogram with equal sides). If we draw the diagonals, isosceles triangles are formed (where the median is also an angle bisector and perpendicular to the base). Since the diagonals of a parallelogram bisect each other, and the diagonals don't bisect the vertex angles where they are drawn, then the parallelogram is not a rhombus.

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