Learn around the properties of parallelograms consisting of relationships amongst opposite sides, the opposite angles, adjacent angles, diagonals and also angles formed by diagonals.
You are watching: Opposite angles in a parallelogram are congruent
Basic properties of Parallelograms
Parallelogram: A quadrilateral v two bag of parallel lines.
To start off with basic rules, opposite political parties of a parallel are always equal length and parallel.
Inside a parallelogram, opposite angles are constantly congruent. Angle that lie alongside each other are constantly supplementary (add as much as 180 degrees).
Diagonals in Parallelograms
The diagonals in a parallelogram bisect each other.
When the diagonals room drawn, this creates plenty of angles that follow the exact same rules as carry out the angles created by two parallel currently intersected through a transversal. A diagonal acts together a transversal and creates alternative interior angles v the parallel sides.
When both diagonals room drawn, two pairs the congruent vertical angles space formed.
When one diagonal line is attracted in a parallelogram, two congruent triangles space formed.
When two diagonals are attracted in a parallelogram, two pairs of congruent triangles space formed.
Rectangles, rhombuses and also squares space special types of parallelograms. Therefore, the exact same rules for angles, sides and diagonals space true for squares and also rectangles also. However, this three forms have additional properties the make lock special.
Let’s walk over parallelograms.
We currently drew parallel
It’s referred to as a parallelogram since there space two pairs of parallel sides.
Besides these two pairs the sides being parallel, lock are also congruent.
The other method to pair the angles is to do them supplementary.
Angles that are adjacent or next to each other add up to
Angles throughout from each various other are congruent. And also if castle are next to eaach other, they add up to
Let’s watch what happens once we draw diagonals.
Let’s draw a diagonal from
Diagonals in reality bisect each other.
Something else that happens once we draw this diagonal is that affects the angles.
Let me expand this diagonal line and also these lines.
See more: How Many Calories In A Mountain Dew : Calories, Nutrition Facts
Let’s watch at these red lines. We’ll view that there space parallel lines and they room intersected through a transversal.