Answer:
Step-by-step explanation:
<ACB = <ECD
These 2 angles are vertically opposite and are equal.
<B = <D
They are both right angles are therefore equal.
The answer is the AA postulate.
A
Note
ASA is a congruence postualate. If S is between two angles that can be shown to be corresponding and equal, then you will have 2 congruent triangles.
SSS if three sides of 1 triangle = 3 sides of a second triangle, then the 2 triangles are congruent. If the the three sides of one triangle are in a ratio with 3 sides of the other triangle, then the triangles could be similar, but that is not the case here.
SAS this is the terminology for congruence as well. We don't know enough to use it for similarity. Some sort of ratio would have to be mentioned to do that.
You are intended to use AA as your answer.
The question is asking us to find the dimensions of the rectangle, which would be the length and width. So, to find this, we must first state our givens, as it is Geometry.
Given: Length of rectangle = 59 + twice the width, diagonal = 2 inches longer than the width
Let's first translate all our givens to numbers. We'll start off by assigning variables that are easy to work with (x, y and z).
x = width
y = length
z = diagonal
Now that we have done that, we need to translate all our givens into numbers. Here is how that would look like:
y = 2x + 59 ←59 plus twice the width (x)
z = y + 2 ←Diagonal = 2 inches more than width
If we draw a diagram, we can see that the diagonal, length, and width all create a right triangle, which means that we can use the Pythagorean Theorem. By using right triangle postulates and theorems, we can deduce that the diagonal is the hypotenuse. Here is what our setup looks like:
x² + y² = z²
<em />Now, all we need to do is plug in the expressions we created for y and z:
x² + (2x + 59)² = [2 + (2x + 59)²]
When we solve for x, we get x = 20. Now, we just plug the x value back into the y equation to get 99. Therefore, the length equals 99 inches and the width equals 20 inches. Hope this helps and have a great day!
It equals 96. hope that helped
