Answer:
If I am correct both figures are similar because of AA (angle reasoning). They have the same angles meaning they are similar triangles even if they don't fit the SSS, SAS, etc. reasoning
Step-by-step explanation:
You could also do the cross multiply divide method to determine if they equal the corresponding length (which they do!) hope this helps! :)
edit: Question 4) is similar following the AA statement for triangles
Question 5 is not similar because it doesn;t match doing the cross multiply divide and has two right angles because they are
rectangles!
Question 1) Corresponding angles are related in two similar figures because they are the same. In triangles two figures similarity can be determined by identifying if they share two angles.
Question 2) Corresponding side lengths can determine the similarity by proving that the shape was only transformed by a scale factor and did not alter shape.
Question 3) No, not neccesarily. If they are the same size, length, and shape they are congruent. Similar figures are altered and different based on a scale factor
Let's consider two prime numbers where each is larger than 2
Say the primes 7 and 11. Adding them gets us 7+11 = 18. This counter example disproves the initial claim since 18 = 9*2 = 6*3 making 18 composite (not prime)
In general, if we let p and q be two primes such that q > p > 2 and q is the next prime after p, then p and q are both odd. If any of them were even then they wouldn't be prime (2 would be a factor)
Adding any two odd numbers together leads to an even number
Proof:
p = 2k+1 where k is some integer
q = 2m+1 where m is some integer
p+q = 2k+1+2m+1 = 2(k+m) + 2 = 2(k+m+1) which is in the form of an even number
That proof above shows us that adding any prime larger than 2 to its next prime up leads to an even number. This further shows us that the claim is false overall. It is only true if you restrict yourself to the primes 2 and 3, which add to 5. Otherwise, the claim is false.
Answer:
64/49 or 1 and 15/49
Step-by-step explanation:
1. process of exponents turns it into 8/7 ^2
2. Solve and simplify
Answer:
to get to 2/3 from 1/12, add 7/12 to 1/12.
Step-by-step explanation:
8/12 is equivalent to 2/3