In ▱ ABCD, equilateral △ ade and equilateral △ BCF are made inward with AD and BC as sides respectively, connecting be and DF. It is proved that the quadrilateral BEDF is a parallelogram

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• 1. In the parallelogram ABCD, take ad and BC as sides, make positive △ ade and positive △ BFC outward respectively, connect dB and EF at point O, and prove that the quadrilateral debf is a parallelogram
• 2. Given the parallelogram ABCD, take ad BC as the edge, make positive △ ade and positive △ BCF outside the parallelogram, connect BD and EF, and they intersect at O, and prove EO = fo, do = Bo There is no picture
• 3. Given the parallelogram ABCD, make the equilateral triangle ade and equilateral triangle BCF outward with AD and BC, connect be and DF, and find be = DF
• 4. The two diagonals of quadrilateral ABCD are perpendicular to each other and intersect at O. given AC = 4cm, BD = 5cm, find the area of quadrilateral ABCD
• 5. The length of diagonal lines AC and BD of quadrilateral ABCD are m and N respectively. It can be proved that when AC ⊥ BD (as shown in Figure 1), the area of quadrilateral ABCD is s = 12mn. Then when the acute angle between AC and BD is θ (as shown in Figure 2), the area of quadrilateral ABCD is s = () A. 12mnB. 12mnsinθC. 12mncosθD. 12mntanθ
• 6. If the area of parallelogram ABCD is 100, then s △ PAB + s △ PCD =
• 7. It is known that the area of parallelogram ABCD is s, and the area of triangle PAB and triangle PCD are S1 and S2 respectively If point P is outside the parallelogram ABCD, then S1 + S2 -- half s Please explain why
• 8. As shown in the figure, in the pyramid s-abcd, the bottom surface ABCD is a parallelogram, the side SBC ⊥ the bottom surface ABCD, ∠ ABC = 45 °, SA = sb, proving that SA ⊥ BC
• 9. Given any parallelogram ABCD, e is the midpoint of AD, f is the midpoint of BC, the proof is: ab + DC = 2ef
• 10. In the parallelogram ABCD, m and N are the midpoint of DC and BC respectively. The known vectors am = C and an = D are used to represent the vectors AB and AD
• 11. It is known that, as shown in the figure, the quadrilateral ABCD is a parallelogram, and both △ ade and △ BCF are equilateral triangles
• 12. As shown in the figure, ABCD is a parallelogram, EF is parallel to ac. if the area of the triangle is 4 square centimeters, calculate the area of the triangle CDF?
• 13. In the parallelogram ABCD, make a straight line AF through a, cross BC and E, and cross DC extension line to F. it shows that the area of triangle ABF and ade is equal
• 14. In the parallelogram ABCD, a straight line AF passing through point a intersects point BC and point E, and a DC extension line intersects point F, which indicates that the areas of △ ABF and △ ade are equal thinking Yes
• 15. In a parallelogram ABCD, a straight line AF passing through point a intersects point BC at point E, and a DC extension line intersects point F. try to explain that the area of △ ABF and △ ade is equal
• 16. In the parallelogram ABCD, BC = 2Ab, e is the midpoint of BC, then ∠ AED=______ ．
• 17. In the parallelogram ABCD, BC = 2Ab, e is the midpoint of BC, then ∠ AED=______ ．
• 18. In the parallelogram ABCD, BC = 2Ab, e is the midpoint of BC, then ∠ AED=______ ．
• 19. ）(1) As shown in Figure 10, in the parallelogram ABCD, BC = 2Ab, e is the midpoint of the BC side, and the degree of ∠ AED is calculated. (2) as shown in Figure 11, e is the square ab ）(1) As shown in Figure 10, in the parallelogram ABCD, BC = 2Ab, e is the midpoint of BC side, and the degree of ∠ AED is calculated (2) As shown in Figure 11, e is a point in the square ABCD, and △ Abe is an equilateral triangle. Think about the relationship between ∠ CED and ∠ CEB, and explain the reason (3) As shown in Figure 12, the height and perimeter of the isosceles trapezoid ABCD are determined by the upper bottom ad = 1, the lower bottom BC = 3 and the diagonal AC ⊥ BD file:///C:/Documents%20and%20Settings/Administrator/Local%20Settings/Temporary%20Internet%20Files/ Content.IE5/3YP2UMUP/image035%5B1%5D .jpg
• 20. In the parallelogram ABCD, BC = 2Ab, e is the midpoint of BC, then ∠ AED=______ ．