Proof: the area of the diamond is equal to half of the product of two diagonals
It is proved that in diamond ABCD, ∵ AC ⊥ BD, ∵ s = s △ ABC + s △ ADC = 12ac · ob + 12ac · od = 12ac (OB + OD) = 12ac · BD. (9 points)
RELATED INFORMATIONS
- 1. Is the area of a diamond equal to half of the product of diagonals?
- 2. What is the sum of squares of a sequence Simple and basic
- 3. The number sequence of senior two It is proved by mathematical induction that "when n belongs to n *, 11 ^ (n + 2) + 12 ^ (2n + 1) can be divisible by 133". When n = K + 1, the formula 11 ^ [(K + 1) + 2] + 12 ^ [2 (k + 1) + 1] can be transformed into________ .
- 4. How to prove this series inequality by mathematical induction It is known that an + 1 (refers to the N + 1st term) = an + (an ^ 2) / (n ^ 2), A1 = 1 / 3. To prove an > 1 / 2 - 1 / 4N. In addition, I will reduce the inequality to a more strict one, and it is better to prove an > 1 / 2 - 1 / 5N first. What is the reason?
- 5. Let {an} and {BN} which are all positive numbers satisfy the following conditions: 5 ^ an, 5 ^ BN, 5 ^ an + 1 is equal ratio sequence, lgbn, lgan + 1, lgbn + 1 is equal difference sequence, and A1 = 1, B1 = 2, A2 = 3. Guess an = n (n + 1) / 2 BN = (n + 1) * (n + 1) / 2 if we use mathematical induction, how to write when n = K + 1?
- 6. Mathematical induction and sequence Observe the following formula: 1=1^2 2+3+4=9=3^2 3+4+5+6+7=5^2 4+5+6+7+8+9+10=7^2 The general law provided by equation is deduced and proved by mathematical induction
- 7. Find the sequence A1 = 1 an + 1 = (2An) / (2 + an) find the general term formula and prove it by mathematical induction
- 8. It is known that the sum of the first n terms of the sequence an = 1 / (3 ^ n-n-1) is SN. It is proved that Sn < 2 holds for any n ∈ n +
- 9. Given sequence Sn = 2An + (- 1) ^ n n is greater than one, try to prove that for any m greater than 4, 1 / A4 + 1 / A5 + 1 / A6 +. + 1 / am is less than 7 / 8 I calculate an = [2 ^ (n-1) - 2 (- 1) ^ n] / 3
- 10. Given the sequence an = 1 / (3 ^ (n-1)), the sum of the first n terms is SN. It is proved that for all n ∈ n *, Sn
- 11. Verification: the area of diamond is equal to half of the diagonal product (two answers)
- 12. Proof: the area of the diamond is equal to half of the product of two diagonals
- 13. How many times is the sum of the squares of the two diagonals of the diamond equal to the square of one side?
- 14. If the side length of a diamond is 2, then the square sum of the two diagonals of the diamond is 2______ .
- 15. If the side length of a diamond is 2, then the square sum of the two diagonals of the diamond is 2______ .
- 16. If the side length of a diamond is 2, then the square sum of the two diagonals of the diamond is 2______ .
- 17. If the side length of a diamond is 2, then the square sum of the two diagonals of the diamond is 2______ .
- 18. Prove that the sum of squares of four sides of a parallelogram is equal to the sum of squares of diagonals
- 19. Proof: the square sum of two diagonals of a parallelogram is equal to the square sum of four sides
- 20. Verification: the sum of squares of two diagonals of a parallelogram is equal to the sum of squares of four sides