# KutaSoftware: Geometry- Properties Of Trapezoids Part 2 (2023)

## Introduction

Free worksheet at www.kutasoftware.com/freeige.html

Go to ➡️ maemap.com/math/geometry/ ⬅️ for more Geometry information!

Happy learning! 💜

## Content

In this video we're going to finish the properties of trapezoid worksheet on the cuda software website, I'll leave a link in the description below.

So you know how to access this free worksheet in this next section we're going to solve for X.

Each figure is a trapezoid and number 11 we're solving for x, and we can see that M n is the median.

That means that M n is equal to one-half.

The sum of the bases of the trapezoid and the bases are the lines that are parallel to one another.

So that's going to be V, U and W T.

So we're going to sum the length of V, U and W t take half of that and not will equal.

Our median of the trapezoid MN m n is negative, x, plus 21 and that's equal to 1/2 times V U, which is 11 plus W T, which is 17 so negative, x, plus 21 equals 1/2 times 11 Plus 17, which equals 28 so the opposite of X plus 21 equals 1/2 times 28 or 28, divided by 2, which is 14 next I'll subtract 21 from both sides to get that negative x or the opposite of X is equal to 14 minus 21, which is negative 7 then I'll just multiply both sides by negative 1.

In order to get a positive x value, negative 1 times negative x is a positive, x and negative 7 times negative 1 is a positive 7x equals 7 in number 11.

This time my x value is in one of the bases, so my median L K equals 1/2 times the sum of the bases which is YX, +, ZW, L K is 29 and that is equal to 1/2 times YX, which is 23 + ZW, which is 11 X plus 2.

For my next step, I'm going to multiply both sides by 2 in order to get rid of this fraction 1/2 and, at the same time, I'm going to combine my like terms with in the parentheses.

So that's going to be the 23 and the to 2 times.

29 is 58 and that's equal to 1/2 times 2, which is 1 times 23 plus 2, which will be 25, plus 11x subtracting 25 from both sides.

I'll get that 33 is equal to 11 X.

My next step is to divide both sides by 11.

33 divided by 11 is 3, so 3 equals x and number 12 and number 13 EC is 20, so this diagonal is 20 and the other diagonal FD is 5.

X minus 10, remember for an isosceles, trapezoid and isosceles is where the bases are parallel, which makes it a trapezoid and the sides that are not the bases are congruent.

So since this is indeed an isosceles trapezoid, we know that the diagonals are congruent or equal in measure, so EC equals FD and if EC equals FD.

That means that 20 is equal.

5X minus 10, adding 10 to both sides, we'll get that 30 is equal to 5x and when we divide both sides by 5 30 divided by 5 is 6 and 6 is equal to 5, divided by 5, which is 1 times X, which is X, so 6 equals x and number 13 and number 14.

We are given consecutive interior angles since ad is parallel to BC, so the consecutive interior angles are supplementary.

That means that a plus B equals 180, a is 11 X, plus 8 and B is 95 that is equal to 180.

My next step, I'll combine my like terms, which is my 8 and my 95, so 11 X, plus 8 plus 95, which is 103.

You equals 180, subtracting, 103 I'll, get that 11.

X is equal to 77 and finally, dividing by 11 will give me the X is equal to 77, divided by 11, which is 7.

So 7 is my solution at number 14.

Lastly, for this set of directions, number 15, looking at number 15, we can see that we have an isosceles trapezoid.

That means that angle is adjacent to the same base are congruent.

So angle, s is congruent to angle.

P and angle.

Q is congruent to angle R and, if angle Q is congruent to angle R.

That means that R is also 28.

X, minus 11 and s and R are consecutive interior angles and therefore will add up to 180 degrees.

So 51, plus 28 X minus 11 equals 180.

Combining my like terms, 51 and negative 11 51 minus 11 is 40, so 40 plus 28 x, equals 180 subtracting 40 from both sides.

I'll get 28 X equal to 140 and dividing by 28 will give me that X is equal to 140 divided by 28, which is 5 x, equals 5 and number 15.

Now, if I were solving for the measure of angle, Q I would take my value of x, which is 5 and plug it in for the X in the equation for Q and then sauce, and that's what we're going to be doing in the next three problems.

Our directions are to find the length of the angle indicated for each trapezoid, so again we're going to solve for X and then plug X in for the indicated angle and number 16.

Our indicated angle is V and V is equal to 5x, plus 38.

So a measure of angle V equals 5x, plus 38 we're given a nice sauce trapezoid.

So that means that angle T is congruent to angle.

U so angle, U is also 12 X minus 28, and you can see that U and V are consecutive interior angles and are supplementary.

So u plus V, will equal 180 degrees, so you 12x, minus 28, plus V 5x, plus 38 equals 180.

Combining my like terms, I'll combine, 12x, +, 5, X and I'll also combine negative 28 and positive 38.

12X plus 5x is 17 X and that will get added to negative 28 plus 38, which is positive, 10 and that is equal to 180 subtracting 10 from both sides.

I'll get that 17 x, equals 170 and when I divide by 17, we will get that X is equal to 10.

So now I'm going to take that value of x, which is 10 and plug it in for my X for the measure of angle B.

So the measure of angle B equals 5 times, 10 plus 38 5 times 10 is 50, plus 38 is 88.

So the measure of angle V equals 88 degrees in number 16 and number 17 I'm.

Finding the measure of angle R we're given that R is 8x plus 34, and we know that R and Q are supplementary, so Q, which is 6 X minus 20 to plus R, which is 8x plus 34.

Will equal 180 combining my like terms 6x with 8x + 22 with 34 6 X plus 8x is 14 X negative, 22 plus 34 is 12, and that is equal to 180 subtracting 12 from both sides.

My term with X will be isolated on the left, which is 14x and that's equal to 180.

Minus 12, which is 168 dividing both sides by 14 I'll get that X is equal to 168, divided by 14, which is a positive 12.

So, knowing that X is 12 I'm going to take that value of x and plug it in for X in the measure of angle are 8 times, X will be 8 times, 12 and I'm, adding 34 to that quantity.

8 times 12 is 96 and when I add 34 to that I get 130 degrees, so R is equal to 130 degrees and number 17.

And lastly, in this video number 18 I'm defined the length of the base indicated for each trapezoid I'm.

Finding the base vu, which vu is 6, X minus 6.

We know that the median is equal to 1/2.

The sum of the bases FG is our median and that's equal to half of the sum of the bases which is TW and vu.

So FG is 7x: minus 4 and that's equal to 1/2 times T W, which is 38 plus vu, which is 6x minus 6, so I'm going to multiply both sides by 2 at the start, so that, as opposed to distributing this fraction of one half I'll be distributing this whole number.

Two on the left and I will also combine my like terms within my parentheses.

On my right so 2 times, 7x is 14x and we're subtracting 2 times 4, which is 8, that's equal to 38 minus 6, which is 32, plus 6x I'll subtract 6x from both sides to get that 8x minus 8 equals 32.

Then, when I add 8 to both sides, I'll get that 8x equals a positive, 40 and I know that 8 goes in that 40 evenly, so X is going to equal five.

Knowing that X is five I'm going to take that value of five and plug it in for my X in my equation for base vu so six times, X is six times 5 and then we're subtracting 6 6 times 5 is 30.

Minus 6 is 24, so number 18 vu equals 24, and with that we finished the properties of trapezoid worksheet.

Don't forget to subscribe to my channel and like this video, if you haven't done so already each like in subscription.

Let me know that you're finding these videos useful and encouraged me to come out with more videos for you.

So do that, if you haven't already also, if you have any questions or need further clarification on any of the problems that we went over in this video, just leave a comment below and I'll get back to you as soon as I can.

## FAQs

### What are the properties of a trapezoid in geometry? ›

Properties of a Trapezoid

The bases are parallel to each other. The median is parallel to both the bases and its length will be the average of the length of the bases. Sum of all the angles in a trapezoid is equal to 360°. The sum of the angles on the same side is equal to 180°.

How do you solve a trapezoid? ›

Area of a trapezoid is found with the formula, A=(a+b)h/2. To find the area of a trapezoid, you need to know the lengths of the two parallel sides (the "bases") and the height. Add the lengths of the two bases together, and then multiply by the height.

What is an example of a trapezoid shape? ›

A trapezoid is a 4-sided flat shape with one pair of parallel sides called its bases. The height (also called altitude) of a trapezoid is perpendicular to its bases. The other two non-parallel sides are called legs. Examples of trapezoid-shaped objects are flowerpots, handbags, pails, and other architectural things.

What is trapezoid in math? ›

A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.

How many properties does a trapezoid have? ›

Trapezoids have one property that must be obeyed. The property is that it must have one pair of parallel sides. If you are looking at a trapezoid, you will see that it has two flat sides. These flat sides are the sides that are parallel to each other.

What are the answers for area of trapezoid? ›

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

What is the formula for area in trapezoid rule? ›

Derivation of Trapezoidal Rule Formula

Check the first trapezoid has length y0 or f(x0) and height Δx. Area of first trapezoids is given by, (1/2) Δx[f(x0) + f(x1)]. Area of third trapezoid is given by, (1/2) Δx[f(x2) + f(x3)], and so on.

How many shapes are in a trapezoid? ›

A trapezoid must have four sides and one set of parallel sides. If the quadrilateral has two sets of parallel sides it is a parallelogram, which is also classified as a trapezoid by some mathematicians.

What are the bases of a trapezoid? ›

The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases.

Does a trapezoid have right angles? ›

The trapezoid has two right angles.

### Which figure Cannot be a trapezoid? ›

Any other shape can have four sides, but if it does not have (at least) two parallel sides, it cannot be a trapezoid. An easy counterexample is a boomerang, which has exactly four sides, but none of them are parallel.

What shape is always a trapezoid? ›

It can be a rectangle if its opposite sides are equal in length and at right angles to each other. So, all rectangles are trapezoids, but, not all trapezoids are rectangles. It's a parallelogram if both pairs of opposite sides are parallel.

What is a trapezoid always an example of? ›

Â Trapezoids must have 4 sides, so they must always be quadrilaterals.

How many ways can you classify a trapezoid? ›

Because there are three ways to define a trapezoid, there are three correct answers to the question. Your response will reveal the definition you use to classify trapezoids. If you only chose polygon 3, you use the exclusive definition which states that a trapezoid has EXACTLY one pair of parallel sides.

What is trapezoid called? ›

Trapezoids are quadrilaterals that have two parallel sides and two non-parallel sides. It is also called a Trapezium.

Is a triangle a trapezoid yes or no? ›

A triangle is a shape that has three sides and three internal angles, a parallelogram is a quadrilateral (four-sided shape) where both sets of opposite sides are parallel to each other, and a trapezoid is a quadrilateral where only one set of sides is parallel.

Can a trapezoid have 2 parallel sides? ›

No - a trapezoid can have only one pair of parallel sides.

What are the base angles of a trapezoid? ›

A pair of angles that share the same base are called base angles of the trapezoid. In Figure 1, ∠ A and ∠ B or ∠ C and ∠ D are base angles of trapezoid ABCD.

What is a trapezoid for 5th grade? ›

A trapezoid is a quadrilateral with one pair of parallel sides. Two sides of a shape are parallel if lines placed along them never cross. In a quadrilateral, parallel sides must be opposite sides. This means they do not share a vertex.

What grade do you learn trapezoids? ›

Trapezoids - 3rd Grade Math - Class Ace.

### What is a 3D trapezoid called? ›

A trapezoidal prism is a 3D figure made up of two congruent trapezoids that are connected by four rectangles. The trapezoids are on the top and the bottom. Thus, they form the base for prisms and have polygons that form their bases. The four rectangles form the lateral faces of the trapezoid prism.

What is a trapezoid shape 3rd grade? ›

A trapezoid is a quadrilateral with one pair of parallel sides. Two sides of a shape are parallel if lines placed along them never cross. In a quadrilateral, parallel sides must be opposite sides. This means they do not share a vertex.

What is a unique trapezoid? ›

The only special feature of a trapezoid that is awarded its own distinctive name is the second pair of parallel sides, which makes the special trapezoid a parallelogram.

Is A trapezoid a polygons? ›

They don't need to have parallel lines or right angles. If you think about that, it means that a triangle is a polygon. So are squares, rectangles and, yes, quadrilaterals, parallelograms and trapezoids. They all are closed shapes with many sides, so they're all polygons!

What angles are congruent in a trapezoid? ›

each pair of base angles are congruent. its diagonals are congruent.

Are all sides of a trapezoid congruent? ›

No sides need to be congruent and no angles need to be congruent. Nothing special happens with the diagonals. A special trapezoid is the isosceles trapezoid (like an isosceles triangle)... The bases (top and bottom) of an isosceles trapezoid are parallel.

Do all trapezoids have equal angles? ›

A trapezium, also known as a trapezoid can have either zero or two pairs of equal angles. If the two non-parallel sides are not the same length, all four angles will be different. If these two sides are equal in length, then there will be two pairs of angles that are the same.

Are all angles of a trapezoid equal? ›

Explanation: All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other. Similarly, the two bottom angles are equal to each other as well.

Can a trapezoid have no lines of symmetry? ›

An isoscles trapezoid has one line of symmetry. If it is not an isosceles trapezoid, it has no lines of symmetry.

What kind of trapezoid has no sides equal? ›

Isosceles trapezoid - trapezoids in which the non-parallel sides have the same length. Scalene trapezoid - this type of trapezoid has four sides that are all of an unequal length.

### Is kite a trapezoid? ›

Whether or not a kite is a trapezium depends on the shape of the kite. In the following image of a typical kite shape, the form is a trapezium since no two sides are parallel to each other. However, a kite can be a trapezoid, which is the case when it's a rhombus.

Is every trapezoid a quadrilateral? ›

Trapezoids are four-sided polygons, so they are all quadrilaterals.

What are the rules for trapezium angles? ›

All trapezium angles (just as in other quadrilateral shapes) add up to 360°. This means that all four angles within a trapezium will add up to this amount, and won't exceed it. Out of the four angles, the two that are adjacent to one another are supplementary; this means that they'll add to 180° (both are 90°).

What is the difference between a trapezoid and a trapezium? ›

In the US and Canada a quadrilateral shape with at least one pair of parallel sides is known as a trapezoid. This is what is called a trapezium outside those countries. However, some suggest that in the US and Canada a trapezoid has one pair of parallel sides and a trapezium has no parallel sides.

What are the 6 properties of an isosceles trapezoid? ›

Properties of Isosceles Trapezium
• Property 1: Only one pair of sides are parallel. ...
• Property 2: Non-parallel sides (legs) are equal in measure. ...
• Property 3: The diagonals are equal in measure. ...
• Property 4: The base angles are equal in measure. ...
• Property 5: The opposite angles are supplementary.

What are the different types of trapezoids? ›

There are three main types of trapezoids: Right trapezoid - these trapezoids have a pair of right angles. Isosceles trapezoid - trapezoids in which the non-parallel sides have the same length. Scalene trapezoid - this type of trapezoid has four sides that are all of an unequal length.

What 3 factors can prove a trapezoid is an isosceles trapezoid? ›

In order to prove that a trapezoid is an isosceles trapezoid, prove each of the following:
• The diagonals are equal.
• Each pair of base angles is equal.
• Each pair of opposite angles is supplementary.
Nov 22, 2021

Is a trapezoid a parallelogram? ›

A trapezoid has one pair of parallel sides and a parallelogram has two pairs of parallel sides. So a parallelogram is also a trapezoid.

Which shape is not a trapezoid? ›

Similarly, if the shape has two sets of parallel sides, it's not a trapezoid. It's either a rectangle, a parallelogram shape or a rhombus.

What are the parts of a trapezoid? ›

A trapezoid is necessarily a convex quadrilateral in Euclidean geometry. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases.

### What are all the areas of trapezium? ›

The area of a trapezium is the average length of its parallel sides multiplied by the perpendicular height. This is shown by the formula 𝑨 = ½ (𝒂 + 𝒃)𝒉.

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