Isosceles Trapezoid Diagonal Properties Practice Problems

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:

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

$x=30$

Let's recall that in an isosceles trapezoid, the sum of the two angles on each of the trapezoid's legs equals 180 degrees.

In other words:

$A+C=180$

$B+D=180$

Since angle D is known to us, we can calculate:

$180-50=B$

$130=B$

To solve this problem, we'll follow these steps:

• Step 1: Define the geometric properties of a trapezoid.
• Step 2: Define the geometric properties of an isosceles trapezoid.
• Step 3: Conclude whether an isosceles trapezoid has two pairs of parallel sides based on these definitions.

Now, let's work through each step:
Step 1: A trapezoid is defined as a quadrilateral with at least one pair of parallel sides.
Step 2: An isosceles trapezoid is a special type of trapezoid where the non-parallel sides (legs) are of equal length. Its defining feature is having exactly one pair of parallel sides, which is the same characteristic as a general trapezoid.
Step 3: Since the definition of a trapezoid inherently allows for only one pair of parallel sides, an isosceles trapezoid, as a type of trapezoid, cannot have two pairs of parallel sides. A quadrilateral with two pairs of parallel sides is typically designated as a parallelogram, not a trapezoid.

Therefore, the solution to the problem is that isosceles trapezoids do not have two pairs of parallel sides. No.

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

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

$22=3+3+7+CD$

$22=CD+13$

$22-13=CD$

$9=CD$