Answer:
See proof below
Step-by-step explanation:
Two triangles are said to be congruent if one of the 4 following rules is valid
- The three sides are equal
- The three angles are equal
- Two angles are the same and a corresponding side is the same
- Two sides are equal and the angle between the two sides is equal
Let's consider the two triangles ΔABC and ΔAED.
ΔABC sides are AB, BC and AC
ΔAED sides are AD, AE and ED
We have AE = AC and EB = CD
So AE + EB = AC + CD
But AE + EB = AB and AC+CD = AD
We have
AB of ΔABC = AD of ΔAED
AC of ΔABC = AE of ΔAED
Thus two sides the these two triangles. In order to prove that the triangles are congruent by rule 4, we have to prove that the angle between the sides is also equal. We see that the common angle is ∡BAC = ∡EAC
So triangles ΔABC and ΔAED are congruent
That means all 3 sides of these triangles are equal as well as all the angles
Since BC is the third side of ΔABC and ED the third side of ΔAED, it follows that
BC = ED Proved
Answer:
The sets E' and P' are not disjoint.
Step-by-step explanation:
Definition: Two sets are disjoint if their intersection is an empty set.
The sets are defined as follows.
We are to determine if the sets E' and P' are disjoint.
E' and P' are the complements of E and P respectively.
Therefore:
The intersection
Therefore, the sets E' and P' are not disjoint.
Answer:
id say the big triangle and the rectangle
Step-by-step explanation:
sorry if im wrong
To solve that we first need to write it as an equation where x is the number:
85 + x^2 = (x-17)^2
85 + x^2 = x^2 - 34x + 289
Now organize the equation by gathering like terms in the same side lf the equation:
You can shift 85 to the other side by subtracting 85 from both sides of the equation:
85 - 85 + x^2 =x^2 34x +289 - 85
x^2 =x^2 + 34x +204
And shift x^2 to the other side by subtracting x^2 from both sides:
x^2 - x^2 =x^2 -x^2 + 34x +204
0 = 34x + 204
Shift 34x to the other side by subtracting 34x from sides
-34x = 34x - 34x + 204
-34x = 204
And now isolate x by dividing both sides of the equation by -34
-34/-34x = 204/-34
x = -6
Thats your awnser , the number is -6
I hope you understood my brief explanation...
I think it is the first one
Hope my answer help?
