Master the 7 pillars of school success that I have learned from 25 years of teaching.
Improve your grades and lower your stress
Welcome to MooMooMath. Today we are going to look at the properties of a rectangle. Before we do that let me throw up the diagram that I have. Rectangles fall under the family of parallelograms and if it is a parallelogram it is also a quadrilateral. So it is a branch off the parallelogram and so a rectangle has every property that a parallelogram has. So let’s review those properties. The opposite sides are congruent, meaning they are the same length. Opposite angles are congruent, opposite sides are parallel, and the adjacent angles are supplementary. A rectangle has all these properties but a couple more. So let’s mark the diagram up to represent these properties. The opposite sides are congruent GA and EM are congruent and I will go ahead and put numbers with it. This side is three and that side is three, and AM is congruent ( equal) to GE,these two sides are congruent , so we will give this on a 5 and that one a 5, so you can see opposite sides are congruent. You can also see opposite angles are congruent, and this is where a rectangle is different ,90 degrees,90 degrees, the opposite angles are congruent to each other, the opposite sides are also parallel, meaning GA is parallel to EM and AM is parallel to GE and the adjacent angles that are next to each other are supplementary ( add to 180) 90 plus 90 add to 180 so we can see the two angles next to each other add to 180 ( supplementary).Now a rectangle has a couple other extra properties, they do have all the properties of a parallelogram but they also have the four right angles that distinguish it as a rectangle and the diagonals have two special properties. The diagonals are congruent to each other. So if draw lines across from corner to corner those two diagonals will be congruent, and the diagonals also bisect forming pairs of congruent triangles. So let me show you that concept. So if I draw a diagonal from A to E that segment is equal to EM those two segments are congruent to each other. So the diagonals are the same length. Also they bisect each other so all four of these are congruent to each other, and as you can see we have pairs of congruent triangles. Triangle AM and the center triangle AMC this top triangle is congruent to GCE this bottom triangle and the two triangles on either side are also congruent. So ACE is congruent to ECM this triangle over here. So there are all the properties of a rectangle. Hope this was helpful