<u><em>Answer:</em></u>
SAS
<u><em>Explanation:</em></u>
<u>Before solving the problem, let's define each of the given theorems:</u>
<u>1- SSS (side-side-side):</u> This theorem is valid when the three sides of the first triangle are congruent to the corresponding three sides in the second triangle
<u>2- SAS (side-angle-side):</u> This theorem is valid when two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle
<u>3- ASA (angle-side-angle):</u> This theorem is valid when two angles and the included side between them in the first triangle are congruent to the corresponding two angles and the included side between them in the second triangle
<u>4- AAS (angle-angle-side):</u> This theorem is valid when two angles and a side that is not included between them in the first triangle are congruent to the corresponding two angles and a side that is not included between them in the second triangle
<u>Now, let's check the given triangles:</u>
We can note that the two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle
This means that the two triangles are congruent by <u>SAS</u> theorem
Hope this helps :)
For this case we have a direct variation of the form:

Where,
- <em>k: proportionality constant
</em>
We must find the value of k.
For this, we use the following data:

Therefore, replacing values we have:

Rewriting:

Clearing the value of k we have:

Therefore, the direct variation equation is given by:

Answer:
The quadratic variation equation for the relatonship is:

Answer:
AC is the longest side
AB is the shortest side
Step-by-step explanation:
We can find the third angle
A+B+C = 180
55+80+C = 180
135+C = 180
C = 180-135
C =45
The longest side is opposite the largest angle
B is the largest angle so AC is the longest side
C is the the smallest angle so AB is the shortest side
Answer:
The answer is $36.25
Step-by-step explanation:
First minus $15 from $160
=145
second divide by the amount of friends which is four
so 145 divided by 4 equals 36.25
each ticket cost $36.25
10x -15y=45
9x+15y= 12
19x= 57
x= 3
3(3)+5y= 4
9 + 5y = 4
5y = -5
y = -1
(3,-1)