What is the probability of rolling 2 standard dice which sum to 9?
1 answer:
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Observe the figure below.
Statement Reason
1. AC and BD bisect each other Given
2. AE = EC and BE = ED Definition of bisection
3. Vertical angle theorem
Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".
4. SAS criterion for congruence
5. Corresponding angles of congruent triangles are congruent
6. Converse of alternate interior angle theorem
7. Vertical angle theorem
8. SAS criterion for congruence
9. Converse of alternate interior angle theorem
As, , so
as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".
The easiest way is if it doesn't need to be simplified. Multiply -2.105 by 
. You get the fraction 
. While this is technically the answer, you can simplify this down to 
. Because 421 is a prime number, this can not be simplified any further. Therefore, the solution is .
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