The parts that are missing in the proof are:
It is given
∠2 ≅ ∠3
converse alternate exterior angles theorem
<h3>What is the Converse of Alternate Exterior Angles Theorem?</h3>
The theorem states that, if two exterior alternate angles are congruent, then the lines cut by the transversal are parallel.
∠1 ≅ ∠3 and l║m because we are: given
By the transitive property,
∠2 and ∠3 are alternate interior angles, therefore, they are congruent to each other by the alternate interior angles theorem.
Based on the converse alternate exterior angles theorem, lines p and q are proven to be parallel.
Therefore, the missing parts pf the paragraph proof are:
- It is given
- ∠2 ≅ ∠3
- converse alternate exterior angles theorem
Learn more about the converse alternate exterior angles theorem on:
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Answer:
169
Step-by-step explanation:
13x13=169 in a square all sides are equal
Answer:
13
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
Here [ a, b ] = [2, 6 ]
f(b) = f(6) = 6² + 5(6) - 8 = 36 + 30 - 8 = 58
f(a) = f(2) = 2² + 5(2) - 8 = 4 + 10 - 8 = 6
Hence
average rate of change = 
= 
= 13
There are 2 possibilities for where A can be: one where C is 30° (and A is 60°) and another where C is 60° (and A is 30°). Since it's not specified, we can find both.
30°:
drawing the triangle on a graph, you can see that point C is 4 units above point B, so we know that one side of the triangle is 4. Once we find the other "leg" of the triangle (the one that's parallel to the x-axis), we can just add that value to B to find the x coordinate of A.
If angle C is 30°, using the side ratios of a 30-60-90 triangle, that side is "a√3", and the side we're looking for is a. So, to find a, we just divide 4 by √3. In that case, point A is 4/(√3) units to the right of -2√3. We can rationalize 4/(√3) like this:
(4√3)/3
and then add that to 2√3:
(4√3)/3 + -2√3
(4√3)/3 + (-6√3)/3 = (-2√3)/3
We know that the x-coordinate of A is (-2√3)/3, and the y-coordinate is -1 because B is a right angle and we're just moving horizontally. So, if C is 30° and A is 60°, point A is at ((-2√3)/3, -1).
60°:
in this case, the leg we know is "a" and the leg we're looking for is "a√3". So, we can multiply 4 by √3 to get the distance from B:
4 x √3 = 4√3
4√3 + -2√3 = 2√3
So the x-coordinate of A here is 2√3, and the y-coordinate is still -1: (2√3, -1).
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