Isosceles Trapezoid - Examples, Exercises and Solutions

Given: $∢C=2x$

$∢A=120°$

isosceles trapezoid.

Find x.

Given that the trapezoid is isosceles and the angles on both sides are equal, it can be argued that:

$∢C=∢D$

$∢A=∢B$

We know that the sum of the angles of a quadrilateral is 360 degrees.

Therefore we can create the formula:

$∢A+∢B+∢C+∢D=360$

We replace according to the existing data:

$120+120+2x+2x=360$

 $240+4x=360$

$4x=360-240$

$4x=120$

We divide the two sections by 4:

$\frac{4x}{4}=\frac{120}{4}$

$x=30$

30°

True OR False:

In all isosceles trapezoids the bases are equal.

True: in every isosceles trapezoid the base angles are equal to each other.

True

In an isosceles trapezoid ABCD

$∢B=3x$

$∢D=x$

Calculate the size of angle $∢B$.

To answer the question, we must know an important rule about isosceles trapezoids:

The sum of the angles that define each of the trapezoidal sides (not the bases) is equal to 180

Therefore:

∢B+∢D=180

3X+X=180

4X=180

X=45

It's important to remember that this is still not the solution, because we were asked for angle B,

Therefore:

3*45 = 135

And this is the solution!

135°

Do the diagonals of the trapezoid necessarily bisect each other?

The diagonals of an isosceles trapezoid are always equal to each other,

but they do not necessarily bisect each other.

(Reminder, "bisect" means that they meet exactly in the middle, meaning they are cut into two equal parts, two halves)

For example, the following trapezoid ABCD, which is isosceles, is drawn.

Using a computer program we calculate the center of the two diagonals,

And we see that the center points are not G, but the points E and F.

This means that the diagonals do not bisect.

No

The perimeter of the trapezoid equals 22 cm.

AB = 7 cm

AC = 3 cm

BD = 3 cm

What is the length of side CD?

Since we are given the perimeter of the trapezoid and not the length of CD, we can calculate:

$22=3+3+7+CD$

$22=CD+13$

$22-13=CD$

$9=CD$

9

Below is an isosceles trapezoid.

$∢B=2y+20$

$∢D=60$

Find $∢B$.

To answer the exercise, certain information is needed:

1. In a quadrilateral the sum of the interior angles is 180.

2. The isosceles trapezoid has equal angles.

3. From here it is we know that the sum of the angles adjacent to a side of the trapezoid is 180°.

We turn this conclusion into an exercise:

2y+20+60=180

We add up the relevant angles

2y+80=180

We move the sections:

2y=180-80

2y=100

Divided by 2

y=50

When we substitute Y we get:

2(50)+20=120

And this is the solution!

120°

Shown below is the isosceles trapezoid ABCD.

Given in cm:
BC = 7  

Height of the trapezoid (h) = 5

Perimeter of the trapezoid (P) = 34

Calculate the area of the trapezoid.

Since ABCD is a trapezoid, it can be argued that:

$AD=BC=7$

The formula to find the area will be

$$$S_{ABCD}=\frac{(AB+DC)\times h}{2}$

Since we are given the perimeter of the trapezoid, we can find$AB+DC$

$P_{ABCD}=7+AB+7+DC$

$34=14+AB+DC$

$34-14=AB+DC$

$20=AB+DC$

Now we will place the data we received in the formula to calculate the area of the trapezoid:

$S=\frac{20\times5}{2}=\frac{100}{2}=50$

50

$∢D=50°$

The isosceles trapezoid

What is $∢B$?

130°

Given: $∢A=120°$

The isosceles trapezoid

Find a: $∢C$

60°

Look at the polygon in the diagram.

What type of shape is it?

Trapezoid

Given: $∢A=y+20$

$∢D=50$

trapecio isósceles.

Find a $∢A$

130

¿Los triángulos marcados son isósceles?

$(ΔABE,ΔCED)\text{ }$

True

Given that: the perimeter of the trapezoid is equal to 75 cm

AB= X cm

AC= 15 cm

BD= 15 cm

CD= X+5 cm

Find the size of AB.

20

Given that: the perimeter of the trapezoid is equal to 35 cm

AB= 10 cm

CD= 15 cm

The isosceles trapezoid

Find the sum of the sizes of the sides.

10

The trapezoid ABCD is isosceles.

AD = AE

Calculate angle $\alpha$.

A,B=110.5 | C,D=69.5 | $\alpha=110.5$