Each of the diagonals of a parallelogram divides it into two congruent triangles, as we saw when we proved properties like that the opposite sides are equal to each other or that the two pairs of … [Read more...] about The Diagonals Divide a Parallelogram Into 4 Equal Areas
A quadrangle in which both pairs of opposite sides are parallel to each other is called a parallelogram.
The opposite sides of a parallelogram are equal in size to each other, and the opposite angles are equal - as we will show, using triangle congruence.
Other properties include:
- The diagonals of a parallelogram bisect each other
- Any two adjacent angles are supplementary
Now that we've explained the basic concept of parallelograms in geometry, let's scroll down to work on specific geometry problems relating to this topic.
One of the proofs done by Euclid in his "Elements" book, where he laid the foundation for geometry, is that if you draw lines parallel to the sides of a parallelogram and through any point on the … [Read more...] about Parallel Lines Drawn Through a Point on the Diagonal of a Parallelogram
One of the properties of parallelograms is that any pair of consecutive angles are supplementary. This is a straightforward application of the properties of parallel lines intersected by a transversal … [Read more...] about Parallelograms: Consecutive Angles are Supplementary
A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. One of the properties of parallelograms is that the opposite angles are congruent, as we will now show. Since … [Read more...] about Parallelograms: The Two Pairs of Opposite Angles are Congruent
A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. We will show that in that case, they are also equal to each other.ProblemABCD is a parallelogram, … [Read more...] about Parallelograms: The Opposite Sides are Equal to Each Other
A parallelogram is defined as a quadrilateral with two opposite pairs of sides are parallel. We have said (and proven) that parallelograms have four basic properties:The two pairs of opposite … [Read more...] about Proving a Quadrilateral is a Parallelogram
A line that intersects another line segment and separates it into two equal parts is called a bisector. In a quadrangle, the line connecting two opposite corners is called a diagonal. We will show … [Read more...] about The Diagonals of a Parallelogram Bisect Each Other