Given points A(−2,0), B(−5,3), C(−9,−1), P(7,6), Q(4,0), and R(−4,4), which of the following proves that △ABC~△PQR?
1 answer:
Based on the SSS similarity theorem, △ABC ~ △PQR because AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5 (option D).
<h3>The SSS Similarity Theorem</h3>Two triangles having three pairs of sides that are proportional can be proven to be similar by the SSS similarity theorem.
If the triangle ABC and triangle PQR are similar, their corresponding sides will be proportional, meaning that: AB/PQ = BC/QR = CA/RP.
Therefore, using the distance formula, , the sides of each triangle is found.
Therefore, it shows that:
AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5
Therefore, based on the SSS similarity theorem, △ABC ~ △PQR because AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5 (option D).
Learn more about the SSS similarity theorem on:
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Answer:
24/5
Step-by-step explanation:
The way I think about areas of sectors is a fraction of the pie. You know what percentage of the "pie" (in this case, circle) you want, because they give you the angle of the sector and you know a circle always has 360°. So technically, you're trying to find 48/360 th of the entire area (36). If you're using a calculator, it doesn't matter if you simplify the fraction, but if you're doing it by hand simplifying makes everything a lot easier.
The equation will be:
Area = 24/180 × 36
= 2/15 × 36
= 72/15
= 24/5
I hope this helped! Also, in Khan Academy, when you get an answer wrong/right, you can view their explanation by clicking "hint" or sometimes "see how we did it" shows up.