Which parallelogram has congruent adjacent angles

I love that word. A square can be defined as a rhombus which is also a rectangle — in other words, a parallelogram with four congruent sides and four right angles. A trapezoid is a quadrilateral with exactly one pair of parallel sides. There may be some confusion about this word depending on which country you're in. In India and Britain, they say trapezium ; in America, trapezium usually means a quadrilateral with no parallel sides.

An isosceles trapezoid is a trapezoid whose non-parallel sides are congruent. A kite is a quadrilateral with exactly two pairs of adjacent congruent sides. A rectangle is a parallelogram that has a right angle. Actually, from this little bit of information, you know about all four angles of a rectangle.

A rectangle is a parallelogram, so its opposite angles are congruent and its consecutive angles are supplementary. Recall that the supplement of a right angle is another right angle.

So a rectangle actually has four right angles. Rectangles have some properties that generic parallelograms do not.

One such property is that the diagonals of a rectangle are congruent. I will state that as a theorem and discuss a game plan for the proof. I will leave the details up to you. To prove this theorem, take a look at the rectangle in Figure But which two triangles do you show are congruent? I would recommend that you show? Each diagonal of a parallelogram separates it into two congruent triangles. More classes on this subject Geometry Quadrilaterals: Angles. Search Math Playground All courses.

All courses. Geometry Perpendicular and parallel Overview Angles, parallel lines and transversals. This test for a parallelogram gives a quick and easy way to construct a parallelogram using a two-sided ruler.

Draw a 6 cm interval on each side of the ruler. Joining up the endpoints gives a parallelogram. The test is particularly important in the later theory of vectors.

Then the figure ABQP to the right is a parallelogram. Even a simple vector property like the commutativity of the addition of vectors depends on this construction.

The parallelogram ABQP shows, for example, that. This test is the converse of the property that the diagonals of a parallelogram bisect each other.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram:. This test gives a very simple construction of a parallelogram. Draw two intersecting lines, then draw two circles with different radii centred on their intersection. Join the points where alternate circles cut the lines.

This is a parallelogram because the diagonals bisect each other. It also allows yet another method of completing an angle BAD to a parallelogram, as shown in the following exercise. Complete this to a construction of the parallelogram ABCD , justifying your answer.

Definition of a Rectangle. A rectangle is a quadrilateral in which all angles are right angles. Each pair of co-interior angles are supplementary, because two right angles add to a straight angle, so the opposite sides of a rectangle are parallel. This means that a rectangle is a parallelogram, so:.

The proof has been set out in full as an example, because the overlapping congruent triangles can be confusing. The diagonals of a rectangle are equal. Let ABCD be a rectangle. Thus we can draw a single circle with centre M through all four vertices. If a parallelogram is known to have one right angle, then repeated use of co-interior angles proves that all its angles are right angles.

We can construct a rectangle with given side lengths by constructing a parallelogram with a right angle on one corner. First drop a perpendicular from a point P to a line. We have shown above that the diagonals of a rectangle are equal and bisect each other.