Interior Angles Of A Trapezoid

What is a Trapezoid?
Trapezoid Definitions
Trapezoid Angles
Backdrop of a Trapezoid
Trapezoid Shapes
Types of Trapezoids

Scalene Trapezoid
Isosceles Trapezoid
Correct Trapezoid
Obtuse Trapezoid
Acute Trapezoid

What is a Trapezoid?

A trapezoid is a quadrilateral with one pair of parallel sides. A trapezoid is:

A aeroplane figure (flat)
A airtight figure (it has an interior and outside)
A polygon (straight sides)
A quadrilateral (four straight sides)

To make a trapezoid, you need a triangle. Whatsoever triangle will do: right, birdbrained, isosceles, scalene. Slice off the top of the triangle so the cut is parallel to the bottom of the triangle. You now have a tinier triangle and a trapezoid.

Because the definition merely requires one pair of parallel sides, the other two sides tin be bundled in many ways, creating four interior angles that will ever add up to 360°.

$trapezoid$

Trapezoid Definitions

Nosotros already know a trapezoid is like the lesser part of a triangle if you lot cut off a smaller triangle from it. You tin besides brand a trapezoid from four line segments, or 4 straight objects.

Use annihilation you lot like: uncooked spaghetti, pencils, lollipop sticks; whatever you accept handy. The four straight (linear) objects tin can be four different lengths, or three different lengths (two of them could exist the same).

Lay two of the objects downwardly, or draw 2 line segments, and so they are parallel (equidistant). Brand them horizontal to you. Put the other two objects on the left and right of these ii, or draw them in, then all eight endpoints touch on.

$trapezoid$

There you have it, a trapezoid! The horizontal parts are the bases. The terminal 2 pieces you drew or put downwards (at the left and right ends) are called the trapezoid'due south legs.

Trapezoid Angles

Notice nosotros did not worry about whatsoever of the interior angles, since keeping two sides parallel forces the balance of the trapezoid to fall into place. The angles sort themselves out and add to 360°.

The altitude of a trapezoid is its height. Do not be fooled past the sloping legs -- if they slope, they are longer than the height. Altitude is ever measured from the base (either parallel side) to the other side, at a right angle to the base.

You can draw a perpendicular line anywhere along the base of the trapezoid, and when it touches the opposite, parallel side, its length is the altitude.

Properties of a Trapezoid

Is a trapezoid a parallelogram?

You tin can place any trapezoid if it is a quadrilateral with one pair of parallel sides. Many mathematicians include parallelograms as types of trapezoids because, of course, a parallelogram has at to the lowest degree ane pair of parallel sides. Other mathematicians exclude parallelograms, saying a trapezoid must have exactly i pair of parallel sides.

Some other identifying property of all trapezoids is that whatever two side by side interior angles will be supplementary (add together to 180°).

Trapezoid Shapes

Usually, to be as clear as possible, pictures and drawings of trapezoids show the two parallel sides running horizontally, with the longer side down equally the base of operations. Exist prepared, though, to run into trapezoids in any orientation. A trapezoid tin can be drawn or pictured with either leg at the bottom, or with the shorter parallel side at the bottom.

Because the parallel sides are the only ones that can exist bases, even when the trapezoid is drawn with a leg at the bottom and horizontal, information technology is not a base of operations. It is still a leg.

The base of operations is ordinarily the longer parallel side, merely if the trapezoid is drawn with the shorter parallel side at the bottom, then information technology is the base.

Types of Trapezoids

Since trapezoids can brainstorm life every bit triangles, they share names derived from the kinds of triangles:

Scalene trapezoid -- Started out as a scalene triangle
Isosceles trapezoid -- Began equally an isosceles triangle
Right trapezoid -- Once was a right triangle
Obtuse trapezoid -- Like an obtuse triangle
Acute trapezoid -- Similar an acute triangle

$trapezoid shapes and types$

Scalene Trapezoid

A scalene trapezoid has four sides of unequal length. The bases are parallel only of different lengths. The two legs are of different lengths.

$Scalene Trapezoid$

Isosceles Trapezoid

An isosceles trapezoid has legs of equal length. The bases are parallel only of different lengths.

$Isosceles Trapezoid$

Right Trapezoid

A right trapezoid has i right angle (90°) between either base and a leg.

$Right Trapezoid$

Obtuse Trapezoid

An obtuse trapezoid has 1 interior angle (created by either base and a leg) greater than 90°.

$Obtuse Trapezoid$

Acute Trapezoid

An acute trapezoid has both interior angles (created past the longer base and legs) measuring less than 90°.

$Acute Trapezoid$

Lesson Summary

Using just four lines and four interior angles, we have constructed a trapezoid, learned what makes a trapezoid unique (a pair of parallel sides), what the various parts of the trapezoid are, and the names of five special trapezoids.

Next Lesson:

How to Detect the Surface area of a Trapezoid