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).
Answer:
<h2>117
x
^5
y^
7</h2>
Step-by-step explanation:
<u>Answer:</u>
$142500
<u>Step-by-step explanation:</u>
We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.
Assuming 
to be the salary of the department head, if the total of the two salaries is $190000, we are to find the salary of the president of the University.
We can write an equation in terms of :
Salary of the president of the University = 
= $142500
Answer:
Step-by-step explanation:
It was give that 86% percent of senators support a bill.
We want to determine the fraction of senators that supports the bill.
We just have to convert 86% into a fraction in its simplest form.
We cancel the common factors to obtain the fraction in the simplest form as:
