In today’s geometry lesson, we’re concluding our study of quadrilaterals, by looking in ~ the nature of trapezoids and kites.

You are watching: Does a trapezoid have congruent diagonals

Jenn, Founder centregalilee.com®, 15+ Years experience (Licensed & Certified Teacher)

You’ll find out all the trapezoidal properties essential to find lacking sides, angles, and perimeters.

In addition, we’ll discover kites and also discuss their connected properties.

*Let’s get started!*

## What Is A Trapezoid?

A trapezoid is a square with specifically one pair the parallel sides. The parallel sides are called bases, and also the various other two sides are referred to as legs.

Bases and also Legs the a Trapezoid

And since the bases space parallel, we know that if a transversal cuts two parallel lines, then the consecutive interior angles room supplementary. This way that the lower base angles space supplementary to upper base angles.

Midsegment that a Trapezoid

Additionally, the midsegment that a trapezoid is the segment authorized the midpoints the the legs, and it is always parallel to the bases. Yet even much more importantly, the midsegment actions one-half the amount of the measure of the bases.

And because we understand that the sum of all internal angles in a quadrilateral is 360 degrees, we deserve to use our properties of trapezoids to find lacking angles and sides of trapezoids.

*Cool!*

Now, if a trapezoid is isosceles, then the legs space congruent, and each pair of basic angles room congruent. In various other words, the reduced base angles space congruent, and also the upper base angles are likewise congruent. Likewise, because of same-side inner angles, a lower base angle is supplementary to any type of upper base angle.

Properties of an Isosceles Trapezoid

But there’s one much more distinguishing element about an isosceles trapezoid.

**A trapezoid is isosceles if and also only if that diagonals are congruent**. For this reason if we deserve to prove the the bases room parallel and the diagonals room congruent, climate we know the square is one isosceles trapezoid, as Cool math accurately states.

*In the video clip below*, we’re walk to job-related through several instances including:

## What space The properties Of Kites?

The first thing the pops into everyone’s mind is the toy that flies in the wind in ~ the end of a long string.

But have you ever before stopped come wonder why a kite paris so well?

The way a toy dragon is do has whatever to carry out with mathematics!

In fact, **a dragon is a special type of polygon**.

A dragon is a quadrilateral that has two pairs of continually congruent sides. And also while the opposite sides are not congruent, the opposite angles created are congruent.

Congruent Sides and Angles of a Kite

Moreover, the diagonals of a kite room perpendicular, and the diagonal line bisects the pair that congruent the opposite angles.

See more: What Was The Most Important Contribution Of The Shang Dynasty In China

Perpendicular Diagonals that a Kite

This means, that since the diagonals crossing at a 90-degree angle, we deserve to use our expertise of the Pythagorean organize to uncover the missing side lengths that a kite and also then, in turn, uncover the perimeter the this distinct polygon.

This frame of two pairs of continuous congruent sides, opposite angles congruent, and also perpendicular diagonals is what permits for the toy kite to paris so well.

Gosh, doesn’t it make you desire to get outside and also play?

## Trapezoid nature – class & instances (Video)

41 min

Introduction come trapezoids and kites00:00:31 – What are the nature of a trapezoid**00:05:28**– use the nature of a trapezoid to find sides, angles, midsegments, or determine if the trapezoid is isosceles (Examples #1-4)

**00:25:45**– properties of kites (Example #5)

**00:32:37**– uncover the kites perimeter (Example #6)

**00:36:17**– find all angle in a kite (Examples #7-8)

**Practice Problems**with Step-by-Step remedies

**Chapter Tests**with video clip Solutions