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Known: parallelogram ABCD, diagonal AC.BD The intersection point O, AEC and bed are all equal to 90 degrees Point E is on ad. a, B, C and D are all connected with E E is on the top of AD, sorry
It is proved that: the diagonals of parallelograms are equally divided with each other, and because OE is the center line of the hypotenuse of two RT △ ace and RT △ BDE, OB = od = OE = OA = OC, so a, B, C, D and E are all on the circle with o as the center and OE as the radius. So ∠ DAB + ∠ DCB = 180 ° and because the parallelograms are diagonally equal, ∠ DAB = 90 ° so the parallelograms ABCD are rectangular
RELATED INFORMATIONS
- 1. In the parallelogram ABCD, e is the midpoint of AD, connecting be and CE. If BC = 2Ab, find the degree of ∠ bec
- 2. It is known that in ▱ ABCD, M is the midpoint of edge ad, and BM = cm
- 3. Given that the diagonal of parallelogram ABCD is AC = 21, be is perpendicular to AC and E, be = 5, ad = 7, find the distance between AD and BC
- 4. A number is not only a multiple of eight, but also a factor of eight. What is the number?
- 5. How many meters is 15 yards
- 6. Chickens and rabbits are in the same cage. There are 15 more chickens than rabbits. Chickens and rabbits have 132 feet. How many chickens and rabbits are there?
- 7. Jiajia's desk drawer is 45cm long, 35cm wide and 14cm high. How many square decimeters of wood do you need to make such a drawer?
- 8. A. B, C three people in table tennis, two people in the game, one person watching, each game after the winner to continue to play, the loser for another person on the stage, has been going on like this, the result a won 11 games, B won 9 games, C won 3 games, then c played a total______ Field
- 9. A freight car and a passenger car leave from a and B at the same time and meet each other in four hours. It takes eight hours for the freight car to complete the whole journey, and how many hours for the passenger car to complete the whole journey?
- 10. In the first day of junior high school, a and B ride bicycles from AB to ab. a starts 15 minutes earlier than B. the speed of a and B is faster than B The ratio is 2: when meeting, a walked 6000 meters less than B. It is known that B walked for 1 hour and 30 minutes to find the speed of a and B and the distance between the two places
- 11. It is known that E and F are the midpoint of ladder ABCD, ad and BC respectively. It is proved by vector that EF is parallel to ab
- 12. In quadrilateral ABCD, AB is parallel to CD ∠ DAB = ∠ DCB, ab = 4, BD = 5 ABC:S Quadrilateral ABCD=
- 13. In quadrilateral ABCD, connect AC and BD, angle DAB = angle DCB = 45 °. BD vertical CD. Triangle ABC area 4.5, calculate ab
- 14. In the quadrilateral ABCD, ∠ ADB = ∠ ABC = 105 ° and ∠ DAB = ∠ DCB = 45 ° prove: CD = ab
- 15. As shown in the figure, in the quadrilateral ABCD, ab = ad, AC bisects ∠ BCD, AE ⊥ BC, AF ⊥ CD. If there are triangles congruent with △ Abe in the figure, please explain the reason
- 16. As shown in the figure, in ladder ABCD, AD / / BC, point E is on diagonal BC, and angle DCE = angle ADB, if 1. In the trapezoid ABCD, AD / / BC, point E is on the diagonal BC, and angle DCE = angle ADB. If BC = 9, CD: BD = 2:3, find the length of CE. 2. In the triangle ABC, ah is perpendicular to BC, h, CF is perpendicular to AB, f, D is a point on AB, ad = ah, de / / BC, prove: de = CF 3. After cutting a square from a rectangle, the remaining rectangle is similar to the original rectangle, and find the ratio of the short side to the long side of the original rectangle
- 17. As shown in the figure: in ladder ABCD, ad is parallel to BC, ab = CD = 2, BC = 6, point E is on BD, and angle DCE = angle ADB (1) Find out all the similar triangles in the graph and prove them (2) Let BD = x, be = y, find out the function analytic expression of Y and X (3) When ad = 4, find the length of be
- 18. In trapezoidal ABCD, AD / / BC, ab = CD = 2, BC = 6, point E is on BD, and angle DCE = angle ADB 1) Find out all the similar triangles in the graph and prove them; 2) Let BD = x, be = y, find the analytic expression of Y with respect to x, and write out its domain of definition; 3) When ad = 4, find the length of be
- 19. As shown in the figure, in the right angle trapezoid ABCD, ad ‖ BC, ab ⊥ BC, ∠ DCB = 75 °, the other vertex e of equilateral △ DCE with CD as one side is on the waist ab. (1) calculate the degree of ∠ AED; (2) prove: ab = BC
- 20. As shown in Figure 1, in the rectangular trapezoid ABCD, ad ‖ BC, ab ⊥ BC, ∠ DCB = 75 ° and the other vertex e of equilateral △ DCE with CD as one side is on the waist ab (1) (2) AB = BC; (3) as shown in Figure 2, if f is a point on the line CD, ∠ FBC = 30 °, the value of dffc can be obtained