Trapezoid Practice Problems for 9th Grade - Area & Properties

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

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.

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 follow these steps:

• Step 1: Identify the given dimensions of the trapezoid.
• Step 2: Use the formula for the area of a trapezoid.
• Step 3: Substitute the given values into the formula and calculate the area.

Now, let's work through these steps:

Step 1: We know from the problem that trapezoid ABCD has bases $AB = 5$ and $CD = 8$, with a height of $AD = 4$.

Step 2: The formula for the area of a trapezoid is:
$A = \frac{1}{2} \times (b_1 + b_2) \times h$

Step 3: Plugging in the values:
$A = \frac{1}{2} \times (5 + 8) \times 4 = \frac{1}{2} \times 13 \times 4 = \frac{52}{2} = 26$

Therefore, the area of the trapezoid ABCD is $26$.

Formula for the area of a trapezoid:

$\frac{(base+base)}{2}\times altura$

We substitute the data into the formula and solve:

$\frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5$