In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
It is proved that CN ⊥ be, CH ⊥ DF are made by C respectively, connecting CE and CF, ∵ s △ BCE = 12s, parallelogram ABCD = s △ DFC, ∵ 12 · DF · ch = 12 · be · CN, ∵ be = DF, ∵ CN = ch, ∵ GC bisection ∠ bgd (the point with equal distance to both sides of the angle is on the bisection line of the angle)
RELATED INFORMATIONS
- 1. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
- 2. The quadrilateral ABCD is a diamond. The extension of de perpendicular to ab intersects BA at point E, and DF perpendicular to BC intersects BC at point F. please guess the size of De and DF
- 3. As shown in the figure, in square ABCD, e and F are two points on BD, and be = DF
- 4. In △ ABC, E.F AB.CB G. h is fed to two points on AC, and Ag = GH = HC EG.FH Intersection at point D. proof: a quadrilateral ABCD is a parallelogram
- 5. It is known that the upper middle points of AB and BC on both sides of triangle ABC are E.F. two points on AC are G.H. Ag = GH = HC,; Connect and extend EG.FH It is proved that ABCD is a parallelogram;
- 6. Cut AE = BF = CG = DH on each side of square ABCD, connect AF, BG, CH and De, and intersect a ` B ` c ` d 'in turn. It is proved that quadrilateral a ` B ` c ` d' is a square
- 7. In the isosceles trapezoid ABCD, ab ∥ DC, ad = BC = 5, DC = 7, ab = 13, point P starts from point a and moves to the midpoint C along ad → DC at the speed of 2 unit lengths per second At the same time, point Q starts from point B and moves along Ba to terminal a at the speed of 1 unit length per second. Let the movement time be T seconds (1) When the value of T is, the quadrilateral pqbc is a parallelogram (2) In the whole movement process, when t is the value, the quadrilateral with points B, C, P and Q as the vertex is isosceles trapezoid
- 8. As shown in the figure, in rectangular ABCD, e is the point on BC and F is the point on CD. Given s △ Abe = s △ ADF = 13sabcd, then the value of s △ AEF: s △ CEF is equal to () A. 2B. 3C. 4D. 5
- 9. Let E and f be on the edge BC and CD of rectangular ABCD respectively, and the areas of △ Abe, △ ECF and △ FDA are a, B and C respectively. Find the area s of △ AEF
- 10. Rectangle ABCD, e and F are on BC and CD respectively. The area of triangle Abe, CEF and ADF are 2, 3 and 4 respectively
- 11. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
- 12. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
- 13. It is known that in square ABCD, e is a point on diagonal BD, passing through e, make ef ⊥ BD, intersect BC with F, connect DF, G is the midpoint of DF, connect eg, CG
- 14. In the square ABCD, e is any point on the diagonal BD. if the circumference of the square ABCD is For m, find the perimeter of the quadrilateral EFCG
- 15. It is known that in square ABCD, e is a point on diagonal BD, passing through e, make ef ⊥ BD, intersect BC with F, connect DF, G is the midpoint of DF, connect eg, CG
- 16. 26. Known: as shown in the figure, in square ABCD, e and F are the midpoint of AB and BC respectively, and CE and DF intersect at point G 26. Known: as shown in the figure, in square ABCD, e and F are the midpoint of AB and BC respectively, and CE and DF intersect at point G Verification: ad = AG
- 17. As shown in the figure, e, F, G and H are respectively the middle points of the edges AB, BC, CD and Da of the spatial quadrilateral ABCD. Prove that: 1. Four points e, F, G and H are coplanar 2. BD / / plane efgh 3 People's education a elective course 2-1p118 / 13
- 18. Given that the space quadrilateral ABCD E F G is the midpoint of AB BC CD ad respectively, we prove the efgh parallelogram
- 19. As shown in the figure, in ladder ABCD, ad ‖ BC and EF are the midpoint of AB and AC respectively. Connect EF and intersect AB and CD with G and h to verify: (1) eh = GF; (2) Hg = 1 / 2 (BC-AD)
- 20. If efgh is the inscribed rectangle of rectangle ABCD, and EF: FG = 3:1, AB: BC = 2:1, then ah: AE=______ .