As shown in the figure, in △ ABC, D is the point on AB, and ad = AC, AE ⊥ CD, the perpendicular foot is e, and F is the midpoint of CB

Prove: in △ ACD, because ad = AC and AE ⊥ CD, according to the intersection point of the vertical line and the bottom of the isosceles triangle, we can prove that e is the midpoint of CD, and because f is the midpoint of CB, so EF ∥ BD, and EF is the median line of △ BCD, so EF = 12bd, that is BD = 2ef

RELATED INFORMATIONS

1. As shown in the figure, in the equilateral triangle ABC, the points D E are on AB AC respectively, and BD = AECD intersects be at the point O DF perpendicular be, and the point F is perpendicular to OD = 2of
2. In triangle ABC, we know that D is the midpoint of AB, e is the point on AC, and AE: EC = 2:1, be and CD intersect at O; (1) OC = OD （2）OB：EB=3;4
3. It is known that: as shown in the figure, in the equilateral triangle ABC, points D and E are on AB and AC respectively, and DB = AE, CD intersects be at points o, DF ⊥ be, and point F is perpendicular, 1) prove: ∠ Abe = ∠ BCD:2 ）Verification: od = 2of
4. It is known that, as shown in the figure, in the equilateral triangle ABC, points D and E are on AB and AC respectively, and BD is equal to AE, CD intersects be at point O, DF is perpendicular to be, and point F is To prove that OD is equal to 2of
5. As shown in the figure, the quadrilateral ABCD and aefg are both rhombic, in which point C is on AF, and points E and G are on BC and CD, respectively. If the angle bad = 135 degrees,
6. The quadrilateral ABCD and the quadrilateral aefg are both rhombic. The point E is on the ad side and the point G is on the extension line of the Ba side As shown in Figure 1, BD and CE are their diagonals. The extension line of Ge intersects BD at point Q and DC at point M. verify: GM ⊥ BD
7. Known: as shown in the figure, in the quadrilateral ABCD, ad ‖ BC, BD bisects AC vertically
8. As shown in the figure, the quadrilateral ABCD, cdef and efgh are all square. (1) is △ ACF similar to △ GCA? Talk about your reasons; (2) find the degree of ∠ 1 + 2
9. As shown in the figure, the quadrilateral ABCD, cdef and efgh are all square. (1) is △ ACF similar to △ GCA? Talk about your reasons; (2) find the degree of ∠ 1 + 2
10. Quadrilateral ABCD, cdef, efgh are square, connect AC, AF, Ag, calculate the degree of angle AFB + angle AGB, thank you
11. As shown in the figure, it is known that e is the midpoint of the edge BC of the square ABCD, and the point F is on the edge CD, and ∠ BAE = ∠ FAE
12. If f is any point on BC of square ABCD, AE bisects ∠ DAF intersecting CD and E, the proof is: AF = BF + De Can you get full marks in the senior high school entrance examination? You are only suitable for the analysis of filling in the blanks, but you will never get full marks for the answers. Now I'm sitting on the chair. What you did is wrong!
13. As shown in the figure, in square ABCD, ab = 3, points E and F are on BC and CD respectively, and ∠ BAE = 30 ° and ∠ DAF = 15 ° to calculate the area of △ AEF
14. In square ABCD, be = 3, EF = 5, DF = 4, how many degrees is the angle BAE + angle DCF?
15. As shown in the figure, ABCD is a square, point E is on BC, and DF ⊥ AE is on F. please determine a point G on AE to make △ ABG ≌ △ DAF, and explain the reason
16. As shown in the figure, the side length of square ABCD is 4, which is the midpoint of BC side, f is the point on DC side, and DF = 14dc, AE and BF intersect at G point. Find the area of △ ABG
17. In the parallelogram ABCD, the diagonal lines AC and BD intersect at point O, if AC = 8, BD = 6 What is the value range of AB?
18. In a parallelogram ABCD with an area of 15, if AB = 5, BC = 6, then CE + CF=
19. If the perimeter of parallelogram ABCD is 44cm and ab is 2cm larger than ad, then AB is equal to?
20. It is known that ab = 8 cm, ad = 12 cm, the area of triangle Abe and triangle ADF are respectively One third of the rectangle ab-cd, find the area of triangle AEF