Difficult Math Challenges (page 2)

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1st Property The opposite sides of a parallelogram are congruent. H: ABCD is parallelogram. T: Demonstration: Affirmative 1. 2. Justification 1. Parallel to Parallel Segments. 2. Parallel to Parallel Segments. 2nd property Each diagonal of the parallelogram divides it into two congruent triangles.
1) Determine the area of ​​the following figures (in cm): a) b) c) d) e) 2) We have a 6cm side equilateral triangle. What is the perimeter and what is the area of ​​this triangle? 3) A trapeze has a base smaller than 2, a base larger than 3 and a height of 10. What is the area of ​​this trapeze? 4) Knowing that the area of ​​a square is 36cm², what is its perimeter?
Consider the following ratio:. Note that your means are equal, so it is called continuous proportion. Thus: Continuous proportion is any proportion of equal means. In general, a continuous proportion can be represented by: Third Proportional Given two non-null natural numbers a and b, the third proportional of these numbers is called x such that: Example: Determine the third proportional number 20 and 10.
Addition Considering the complexes:, the sum is obtained by summing their real and imaginary parts separately: = (a + c) + (b + d) i Examples (2 + 3i) + (5 + 4i) = (2 +5) + (3 + 4) i = 7 + 7i 2i + (6 + 9i) = (0 + 6) + (2 + 9) i = 6 + 11i (5 + 3i) + 3 = (5 + 3 ) + (3 + 0) i = 8 + 3i Subtraction Given the complexes, the difference is obtained by subtracting their real and imagined parts separately: = (a - c) + (b - d) i Examples (2 + 3i) - (5 + 4i) = (2 - 5) + (3 - 4) i = -3 - i 2i - (6 - 9i) = (0 - 6) + (2 - (- 9)) i = -6 + 11i (5 + 3i) - 3 = (5 - 3) + (3 - 0) i = 2 + 3i Next: Multiplication and division in algebraic form
In the decimal metric system, we must remember that in transforming surface units, each surface unit is 100 times larger than the next lower unit: Note the following transformations: transform 2.36 m 2 to mm 2. km 2 hm 2 dam 2 m 2 dm 2 cm 2 mm 2 To transform m 2 to mm 2 (three positions on the right), we must multiply it by 1.
Did you know that if someone counted aloud to a million, 24 hours a day, without stopping - 1… 2… 3… - saying a digit or number per second, it would take no less than 12 days to finish the enumeration? The Russian Multiplication Method Table of Contents Next >> Who Discovered the Pythagorean Theorem?