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
In the graph, △ ADF and △ Abe are congruent. ∵ AC bisects ∠ BCD, AF ⊥ CD, AE ⊥ CE; ∵ AF = AE, ∠ AFD = ∠ AEB = 90 ° in RT △ ADF and RT △ Abe, ∵ AB = ADAF = AE, ≌ RT △ ADF ≌ RT △ Abe
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- 1. In the quadrilateral ABCD, ∠ ADB = ∠ ABC = 105 ° and ∠ DAB = ∠ DCB = 45 ° prove: CD = ab
- 2. In quadrilateral ABCD, connect AC and BD, angle DAB = angle DCB = 45 °. BD vertical CD. Triangle ABC area 4.5, calculate ab
- 3. In quadrilateral ABCD, AB is parallel to CD ∠ DAB = ∠ DCB, ab = 4, BD = 5 ABC:S Quadrilateral ABCD=
- 4. 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
- 5. 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
- 6. In the parallelogram ABCD, e is the midpoint of AD, connecting be and CE. If BC = 2Ab, find the degree of ∠ bec
- 7. It is known that in ▱ ABCD, M is the midpoint of edge ad, and BM = cm
- 8. 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
- 9. A number is not only a multiple of eight, but also a factor of eight. What is the number?
- 10. How many meters is 15 yards
- 11. 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
- 12. 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
- 13. 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
- 14. 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
- 15. 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
- 16. 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
- 17. As shown in the figure, if the quadrilateral ABCD is trapezoid, ad ‖ BC, CA is bisector of ∠ BCD, and ab ⊥ AC, ab = 4, ad = 6, then tanb = () A. 23B. 22C. 114D. 554
- 18. In the isosceles trapezoid ABCD, the extension lines of AD / / BC, de / / AC and BC intersect at the point E, CA bisects ∠ BCD, and proves ∠ B = 2 ∠ E
- 19. In trapezoidal ABCD, ad ‖ BC, ab = AC, if ∠ d = 110 °, ACD = 30 °, then ∠ BAC is equal to () A. 80°B. 90°C. 100°D. 110°
- 20. It is known that in the quadrilateral ABCD, AD / / BC, angle BAC = angle D, and point E.F BC.CD And QE AEF = angle ACD