Answer:
A is the y-axis
C is the origin
D is the x-axis
Step-by-step explanation:
I do not know what B is sorry
Given that there is no any option to choose I am going to help you according to the concepts of
Congruent Triangles. Two triangles are congruent if and only if:
1. They have:exactly the same three sides
2. exactly the same three angles.
<span>There are five ways to find if two triangles are congruent but in this problem we will use only two.
First Answer:<u>ASA criterion:</u> </span><em>A</em><span><em>ngle, side, angle</em>. This means that we have two triangles where we know two angles and the included side are equal.</span>
So:
If ∠BAC = ∠DEF and
![\overline{AC}=\overline{DE}](https://tex.z-dn.net/?f=%5Coverline%7BAC%7D%3D%5Coverline%7BDE%7D)
<em>Then ΔABC and ΔEFD are congruent by ASA criterion.</em>
Second answer:<u>SAS criterion:</u> <em>S</em><span><em>ide, angle, side</em>. This means that we have two triangles where we know two sides and the included angle are equal.
</span>
![If \ \overline{AC}=\overline{DE} \ and \ \overline{BC}=\overline{DF}](https://tex.z-dn.net/?f=If%20%5C%20%5Coverline%7BAC%7D%3D%5Coverline%7BDE%7D%20%5C%20and%20%5C%20%5Coverline%7BBC%7D%3D%5Coverline%7BDF%7D)
<em>Then ΔABC and ΔEFD are congruent by SAS criterion.</em>
So we know the total distance is 65 miles.
Let d1 = distance to 1st delivery from distribution center
d2 = distance to 2nd delivery from 1st delivery site
d3 = distance to 3rd delivery from 2nd delivery site
d4 = distance from 3rd delivery site back to distribution center.
So total distance D = d1 + d2 + d3 + d4 = 65
We know that d1 to d2, d2 to d3 and d3 to d4 each differ by 1/2 a mile.
This means that
d2 = d1 + 1/2
d3 = d2 + 1/2 = (d1 + 1/2) + 1/2 = d1 + 1
d4= d3 + 1/2 =d1 + 1 + 1/2 = d1 + 3/2
Adding all these distances:
d1 + d2 + d3 + d4
= d1 + (d1 + 1/2) + (d1 + 1) + (d1 + 3/2)
= 4d1 + 3 = 65
d1 = (65 - 3)/4
So the distance to the first delivery, d1 is (65 - 3)/4.
Does that make sense?
Answer:
c = 9
Step-by-step explanation:
Since angle d and 59 are on a right angle (indicated by the small square)
We can equate the sum of these angles to 90:
d+59=90
Now we subtract 59 from both sides:
d+59-59=90-59
d=31
Since angles d,c and 140 are on a straight line we can equate the sum of these 3 to 180:
c+d+140=180
Substitute d with 31 from previous working out:
c+31+140=180
Simplify:
c+171=180
Subtract 171 from both sides:
c+171-171=180-171
Simplify:
c= 9