As shown in the figure, e and F are two points on the diagonal BD of the quadrilateral ABCD, AE ‖ CF, AE = CF, be = DF
It is proved that ∵ AE ∥ CF ∥ AED = ∠ CFB (3 points) ∵ DF = be, ∵ DF + EF = be + EF, & nbsp; that is, de = BF In △ ade and △ CBF, AE = CF ∠ AED = cfbde = BF (9 points) ≌ △ ade ≌ △ CBF (SAS) ≌ (10 points)
RELATED INFORMATIONS
- 1. As shown in the figure, e and F are two points on the diagonal AC and BD of rectangle ABCD, and AE = DF. Prove the congruent triangle COF of triangle BOE
- 2. As shown in the figure, in square ABCD, ∠ DAF = 25 °, AF intersects diagonal BD at e, intersects CD at F, then ∠ bec=______ Degree
- 3. As shown in the figure, in square ABCD, ∠ DAF = 25 °, AF intersects diagonal BD at e, intersects CD at F, then ∠ bec=______ Degree
- 4. As shown in the figure, in square ABCD, ∠ AFD = 65 ° AF and BD intersect at E
- 5. As shown in the figure, in rectangular ABCD, AF ⊥ BD, perpendicular foot is f, ∠ DAF = 3 ∠ BAF, calculate the degree of ∠ fac
- 6. It is known that e is the midpoint of the waist BC of the trapezoidal ABCD, and ab + CD = ad
- 7. For the isosceles trapezoid ABCD, ad is parallel to BC, ad = 2cm, BC = 8cm, e is the midpoint of the lumbar CD, be divides the trapezoid into two parts, the perimeter difference is 3cm, and calculates the length of ab I only have the second grade of junior high school, and I am learning the median line of triangle and trapezoid. I hope you can help me solve the problem according to the direction of this theorem
- 8. In trapezoidal ABCD, AD / / BC, ab = DC, angle ABC = 80 °, e is the point on lumbar CD, connecting be, AC and AE, if angle ACB = 60 ° and angle EBC = 50 ° Find the degree of the triangle EAC
- 9. As shown in the figure, in the known square ABCD, e is the point on ad, BF bisects ∠ EBC intersects DC at point F
- 10. It is known that in square ABCD, point E is the point above ad, BF bisects ∠ EBC, intersects DC at point F, and the proof is: be = AE + CF
- 11. As shown in the figure, e and F are two points on the diagonal BD of the quadrilateral ABCD, AE ‖ CF, AE = CF, be = DF
- 12. As shown in the figure, in the quadrilateral ABCD, ab = CD, BF = De, AE ⊥ BD, CF ⊥ BD, e and f respectively. (1) prove: △ Abe ≌ △ CDF; (2) if AC and BD intersect at point O, prove: Ao = Co
- 13. Square ABCD, AE + CF = EF, verification ∠ EDF = 45 degree
- 14. As shown in the figure, in square ABCD, ∠ EDF = 45 ° and the two sides of ∠ EDF intersect AB and BC respectively at e and F. try to explore the quantitative relationship between AE, EF and CF, and prove your conclusion
- 15. If the perimeter of a diamond is 8 cm and the height is 1 cm, the ratio of the degrees of the two adjacent angles of the diamond is 0——
- 16. If the perimeter of the diamond is 8 cm and the height is 1 cm, what is the degree ratio of the two collar angles of the diamond?
- 17. If the perimeter of the diamond is 8 cm and the height is 1 cm, what are the degrees of the two adjacent inner angles in the diamond?
- 18. It is known that the perimeter of the diamond is 16cm, and there is an internal angle of 60 degrees, then the shorter diagonal length of the diamond is______ cm.
- 19. If the perimeter of the diamond ABC is 16cm and an internal angle is 30 °, the area of the diamond ABC is
- 20. The perimeter of the diamond is 16cm, and one of its internal angles is 150 degrees?