In today’s geometry lesson, we’re finish our study of quadrilaterals, through looking in ~ the nature of trapezoids and kites.
You are watching: Sum of interior angles of a trapezoid
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You’ll find out all the trapezoidal properties required to find lacking sides, angles, and perimeters.
In addition, we’ll check out kites and discuss their associated properties.
Let’s obtain started!
What Is A Trapezoid?
A trapezoid is a square with precisely one pair the parallel sides. The parallel political parties are referred to as bases, and also the various other two political parties are referred to as legs.
Bases and also Legs the a Trapezoid
And because the bases are parallel, we understand that if a transversal cuts 2 parallel lines, climate the consecutive internal angles are supplementary. This way that the lower base angles are supplementary to upper base angles.
Midsegment the a Trapezoid
Additionally, the midsegment that a trapezoid is the segment involvement the midpoints the the legs, and it is constantly parallel come the bases. However even much more importantly, the midsegment procedures one-half the sum of the measure of the bases.
And because we recognize that the amount of all interior angles in a square is 360 degrees, we can use our nature of trapezoids to find absent angles and also sides the trapezoids.
Now, if a trapezoid is isosceles, then the legs room congruent, and each pair of base angles room congruent. In various other words, the lower base angles are congruent, and also the upper base angle are additionally congruent. Likewise, because of same-side internal angles, a reduced base angle is supplementary to any upper base angle.
Properties of one Isosceles Trapezoid
But there’s one more distinguishing element regarding an isosceles trapezoid.
A trapezoid is isosceles if and only if the diagonals space congruent. Therefore if we can prove the the bases space parallel and also the diagonals room congruent, then we understand the square is one isosceles trapezoid, as Cool math accurately states.
In the video below, we’re walk to job-related through several instances including:Using this properties the trapezoids to find lacking side lengths, angles, and perimeter.Determining if the provided quadrilateral is a trapezoid, and if so, is the trapezoid isosceles?
What are The nature Of Kites?
The first thing that pops right into everyone’s psychic is the toy that paris in the wind in ~ the finish of a long string.
But have actually you ever stopped to wonder why a kite paris so well?
The means a toy dragon is made has whatever to perform with mathematics!
In fact, a kite is a special form of polygon.
A dragon is a square that has two bag of continuous congruent sides. And also while the opposite sides space not congruent, the opposite angles formed are congruent.
Congruent Sides and also Angles of a Kite
Moreover, the diagonals of a kite space perpendicular, and the diagonal bisects the pair of congruent opposite angles.
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Perpendicular Diagonals the a Kite
This means, that because the diagonals crossing at a 90-degree angle, we have the right to use our expertise of the Pythagorean theorem to uncover the missing side lengths the a kite and then, in turn, find the perimeter the this special polygon.
This framework of 2 pairs of continuous congruent sides, opposite angles congruent, and also perpendicular diagonals is what enables for the toy dragon to fly so well.
Gosh, doesn’t it do you want to gain outside and play?
Trapezoid properties – lesson & instances (Video)
41 minIntroduction to trapezoids and also kites00:00:31 – What are the nature of a trapezoid00:05:28 – usage the properties of a trapezoid to uncover sides, angles, midsegments, or determine if the trapezoid is isosceles (Examples #1-4)00:25:45 – properties of kites (Example #5)00:32:37 – discover the kites perimeter (Example #6)00:36:17 – uncover all angle in a dragon (Examples #7-8)Practice Problems through Step-by-Step services Chapter Tests with video clip Solutions