Answer:
The answer to your question is x = 6 and y = 9
Step-by-step explanation:
Data
AB = x DF = 18
BC = 5 FE = 15
AC = 3 DE = y
Process
1.- Find y
Use proportions to find it
DE/FE = AC/BC
Substitution
y/15 = 3/5
Solve for y
y = 15(3/5)
y = 45/5
y = 9
2.- Find x
AB/DF = BC/FE
Substitution
x/18 = 5/15
Solve for x
x = 18(5/15)
x = 90/15
x = 6
In order to simplify, let's add 6x and 13x.
We will get 19x, and that is the answer!
The perimeter is the sum of all its sides.
That is for all triangles or polygons in general.
Good luck!
M.
The answer to one is b. I recommend using a website called Desmos when you have to do things with equations. It has been very helpful to me and gives you the answer automatically. Even teachers recommend it.
Since segment AC bisects (aka cuts in half) angle A, this means the two angles CAB and CAD are the same measure. I'll refer to this later as "fact 1".
Triangles ABC and ADC have the shared segment AC between them. By the reflexive property AC = AC. Any segment is equal in length to itself. I'll call this "fact 2" later on.
Similar to fact 1, we have angle ACB = angle ACD. This is because AC bisects angle BCD into two smaller equal halves. I'll call this fact 3
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To summarize so far, we have these three facts
- angle CAB = angle CAD
- AC = AC
- angle ACB = angle ACD
in this exact order, we can use the ASA (angle side angle) congruence property to prove the two triangles are congruent. Facts 1 and 3 refer to the "A" parts of "ASA", while fact 2 refers to the "S" of "ASA". The order matters. Notice how the side is between the angles in question.
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Once we prove the triangles are congruent, we use CPCTC (corresponding parts of congruent triangles are congruent) to conclude that AB = AD and BC = BD. These pair of sides correspond, so they must be congruent in order for the entire triangles to be congruent overall.
It's like saying you had 2 identical houses, so the front doors must be the same. The houses are the triangles (the larger structure) and the door is an analogy to the sides (which are pieces of the larger structure).
