It is known that, as shown in the figure, e and F are two points on the diagonal AC of the parallelogram ABCD, AE = CF
It is proved that: (1) AF = CE and ABCD are parallelograms, AF = CB, ad ‖ BC. In △ ADF and △ CBE, AF = cead = CB, DAF = BCE, AF = CEA, ADF = CB, DAF = BCE, and ≌ ADF ≌ CBE (SAS). (2) AF = ADF ≌ CBE, DFA = bec. DF ≌ EB
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- 1. As shown in the figure, in the parallelogram ABCD, e is the midpoint of CD, and the extension line of be and ad intersects at point F Million urgent A. still have half an hour to hand in homework a. a a... will add ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD ADD
- 2. In the parallelogram ABCD, e is the midpoint of AD, the extension line of be is at point F, connecting Ce (1), proving: CD = DF (2) if ad = 2CD, please write all right angle triangles in the graph In the parallelogram ABCD, e is the midpoint of AD, the extension line of be is at the point F, connecting Ce (1), proving: CD = DF (2) if ad = 2CD, please write all right triangles and isosceles triangles in the graph
- 3. It is known that in △ ABC, ab = AC, BD = DC, AE bisects ∠ fac, try to guess the position relationship between AE and ad, please explain the reason
- 4. It is known that ab = AC, BD = DC, AE bisects ∠ fac, Q: is AE perpendicular to ad? Why?
- 5. The bisector of the outer angle fac of a triangle is AE, angle 1 equals angle 2, ad equals AC. verify that DC is parallel to Ae
- 6. It is known that E and F are two points on diagonal AC of parallelogram ABCD, and be = DF. It is proved that bfde is a parallelogram
- 7. It is known that EF in parallelogram ABCD is two points on diagonal BD, and be = DF. It is proved that bfde is parallelogram
- 8. It is known that, as shown in the figure, e and F are the triangles of diagonal AC of parallelogram ABCD
- 9. As shown in the figure, the quadrilateral ABCD is a diamond, f is the intersection of a point DF on AB, AC at e. the angle AFD = angle CBE is proved
- 10. As shown in the figure, in the quadrilateral ABCD, ad ∥ BC, ∠ B = 90 °, ad = 16cm, ab = 4cm, BC = 21cm, the moving point P starts from point B and moves to point C at the speed of 2cm / s along the direction of line BC, the moving point Q starts from point a and moves to point d at the speed of 1cm / s along the direction of line ad, and points P and Q start from point B and a respectively. When point P moves to point C, point Q stops moving, and the time of motion is set (1) find the length of DQ (expressed by the algebraic expression of T); (2) when the value of T is, the area of △ PQD is equal to 12cm2? (3) Is there a point P such that △ PQD is a right triangle? If it exists, request all the values of t that meet the requirements; if not, explain the reason
- 11. It is known that, as shown in the figure, e and F are two points on the diagonal AC of the parallelogram ABCD, AE = CF
- 12. It is known that, as shown in the figure, e and F are two points on the diagonal AC of the parallelogram ABCD, AE = CF
- 13. In the parallelogram ABCD, e f is two points on the diagonal AC, and AE = CF
- 14. As shown in the figure: in known quadrilateral ABCD, ab = ad, AE, AF divide ∠ BAC and ∠ CAD equally
- 15. In the known quadrilateral ABCD, ab = ad, AE, AF bisects the angle BAC and the angle CAD respectively
- 16. Known: as shown in the figure, the quadrilateral ABCD is a circle inscribed quadrilateral, e is a point on the diagonal ad, and ab = ad = AE verify: angle CAD = 2 angle CBE
- 17. As shown in the figure, take two points E and F on the diagonal AC of the parallelogram ABCD, if AE = cf. verify: ∠ AFD = ∠ CEB
- 18. As shown in the figure, in the isosceles trapezoid ABCD, ab ∥ CD, CE ∥ Da, known AB = 8, DC = 5, Da = 6, calculate the perimeter of △ CEB
- 19. As shown in the figure, in the isosceles trapezoid ABCD, ab ∥ CD, CE ∥ Da, known AB = 8, DC = 5, Da = 6, calculate the perimeter of △ CEB
- 20. In isosceles trapezoid ABCD, AB / / DC, CE / / DA, known AB = 12, DC = 8, Da = 6, find the perimeter of △ CEB