Given that the straight line of square ABCD passing through point C intersects the extension lines of AD and ab with points E and f respectively, and AE = 10 and AF = 15, the side length of square ABCD is calculated
Let the side length of the square be x, FB ratio FA equal to BC ratio AE is 10-x / 10 = x / 15, get x = 6, extend the intersection of BC and e at k AB = Ke = 6, AE = BK = 15, let CG be Z, get BC / BK = CG / EK, 6 / 15 = Z / 6 with similar triangle, get CG equal to 2.4, draw a picture, and you'll understand it. It's a good trouble to add some points to it!!!
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- 1. In square ABCD, e is the point on AC, EF ⊥ AB, eg ⊥ ad, ab = 6, AE: EC = 2:1. Find the area of quadrilateral afeg
- 2. In square ABCD, e is the point on AC, EF ⊥ AB, eg ⊥ ad, ab = 6, AE: EC = 2:1. Find the area of quadrilateral afeg
- 3. In square ABCD, e is on AC, EF ⊥ AB is on F, eg ⊥ ad is on G, ab = 8cm, AE ratio EC = 3:1, calculate the area of quadrilateral afeg Draw your own picture I can't make it easy
- 4. In square ABCD, e is a point on AC, EF is perpendicular to AB, BG is perpendicular to ad, ab = 6, AE: EC = 2:1, find the area of afeg
- 5. In the quadrilateral ABCD, point E is the midpoint of BC, point F is the midpoint of CD, and AE is perpendicular to AB, AF ⊥ CD, connecting EF to prove AB = ad When AB, CD and BC are related, the △ AEF is an equilateral triangle
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- 7. In the square ABCD, the midpoint e of BC connects AE, and a point F on CD makes EF ⊥ AE connect AF. verify that AF = AD + FC
- 8. Given square ABCD, de ratio EC = 3:2, EF vertical AE, then FC ratio EC = -, EF ratio AE = -, de ratio AE = -
- 9. In rectangular ABCD, points E and F are on line AB and ad respectively, AE = EB = AF = 2 / 3fd = 4. Along the straight line EF, the triangle AEF is folded into triangle a'ef, Make plane a'ef perpendicular to plane bef Finding a '- fd-c cosine of dihedral angle If the points m and N are on the line segments FD and BC respectively, and the quadrilateral mncd is folded upward along the line Mn, so that C and a 'coincide, the length of the line segment FM is calculated
- 10. In the arithmetic sequence {an}, A1 = 3, the sum of the first n terms is Sn, the items of the arithmetic sequence {BN} are all positive, B1 = 1, the common ratio is Q, and B2 + S2 = 12, q = s2b2. (1) find an and BN; (2) let the sequence {CN} satisfy the first n terms and TN of CN = 1sn, {CN}, and prove that TN < 23
- 11. Given the square ABCD, the straight line passing through C intersects the extension lines of AD and ab at points E and f respectively, and AE = 15 and AF = 10, the side length of square ABCD is calculated
- 12. Given the square ABCD, the straight line passing through C intersects the extension lines of AD and ab at points E and f respectively, and AE = 15 and AF = 10, the side length of square ABCD is calculated
- 13. Given the square ABCD, the straight line passing through C intersects the extension lines of AD and ab at points E and f respectively, and AE = 15 and AF = 10, the side length of square ABCD is calculated
- 14. Please read the following materials: problem: as shown in Figure 1, in diamond ABCD and diamond befg, points a, B and E are on the same line, P is the midpoint of line DF, connecting PG and PC. if ∠ ABC = ∠ bef = 60 °, explore the position relationship between PG and PC and the value of pgpc. XiaoCong's idea is: extend GP intersection DC at point h, construct congruent triangle, and solve the problem through reasoning. Please refer to XiaoCong Students' ideas, explore and solve the following problems: (1) write the position relationship between PG and PC and the value of pgpc in the above problem; (2) rotate the diamond BFG in Figure 1 clockwise around point B, so that the diagonal BF of diamond BFG is in the same line with the edge ab of diamond ABCD, and other conditions in the original problem remain unchanged (as shown in Figure 2). Are the two conclusions you get in (1) correct What's the change? Write down your conjecture and prove it. (3) if ∠ ABC = ∠ bef = 2 α (0 °< α< 90 °) in Figure 1, rotate the diamond BFG clockwise at any angle around point B, and other conditions in the original problem remain unchanged, please write down the value of pgpc directly (expressed by the formula containing α)
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- 19. As shown in the figure below, the quadrilateral ABCD is trapezoid, the ratio of the top and bottom is 3:5, and E is the midpoint of the ad side. Calculate the area ratio of the triangle CDE and the quadrilateral abce
- 20. A flat quadrilateral ABCD is divided into a triangle CDE and a trapezoid abce by the line CE, with the height of AF = 6cm. It is known that the area of trapezoid abce is 9cm larger than that of triangle CDE. How many cm is the length of trapezoid AE?