First, multiple-choice questions (3 points for each question, ***30 points)

1. Connect the midpoints of the four sides of a parallelogram in turn with equal diagonal lines, and the resulting quadrilateral must be ().

A. trapezoid B. diamond C. rectangle D. square 2 The point with equal distance to the three sides of a triangle is a triangle ().

A. Intersection of three centerlines B. Intersection of three heights C. Intersection of three angular bisectors D. Uncertainty

3. If the diagonal length of a square is a, it is the distance from the intersection of its diagonal to its diagonal. The side is ().

A.22a B.24a C.a2 D.22a

4. The upper base length of the trapezoid is 4 and the lower base length is 6, so the length of the line segment between the two diagonals of the neutral line is ().

A. 1

5. As shown in the figure, fold the rectangular ABCD paper in half along the diagonal BD, so that the point C falls at C? Office, BC? Cross AD to point e, if, then without any auxiliary line, 45? Make friends ()

A.6 B.5 C.4 D.3

Question 6

6. As shown in the figure, in □ABCD, the cross-diagonal intersection O leads to EF passing through BC at point E and AD at point F. If AB=5cm, AD=7cm, OE=2cm, the circumference of quadrilateral ABEF is ().

a . 14 b . 16cm c . 19cm d . 24cm

7. If the difference between the two bottoms of an isosceles trapezoid is equal to the length of a waist, then the acute angle of this isosceles trapezoid is ().

.60 caliber? B.30？ C.45？ D. 15？

8. Connect the midpoints of four sides of a quadrilateral in turn, and the quadrilateral obtained is a diamond, so the original quadrilateral must be ().

A. parallelogram B. quadrilateral with equal diagonal lines

C. rectangle D. quadrilateral with diagonal lines perpendicular to each other

9. If the median line on the hypotenuse of a right-angled triangle is equal to the shortest right-angled side length, its minimum internal angle is equal to ().

A. 10？ B.20？ C.30？ D.60？

10. Among the following conditions, it is () that can determine that a quadrilateral is a square.

A. the diagonals are equal. Diagonal lines are perpendicular to each other

C. Diagonal lines are equal and vertical. D. Diagonal lines are equal and divided vertically.

Fill in the blanks (3 points for each question, 30 points for * * *)

1 1. The internal angle of an isosceles triangle is 80 degrees? , the other two angles are _ _ _ _ _ _ _.

12.In, then a: b: c = _ _ _ _ _ _.

13. Given that the diagonal length of a rectangle is 10cm, the perimeter of the quadrilateral obtained by connecting the midpoints of its sides is _ _ _ _ _ _ _ _ cm.

14. The lengths of two adjacent sides of a parallelogram are 6 cm and 8 cm respectively, and the included angle is 30? , the area of this parallelogram is _ _ _ _ _ _ _.

15. The ratio of two adjacent angles of a parallelogram is 1:2, and the two heights are 2 and 3 respectively, so its area is _ _ _ _ _.

16. If the circumference of the diamond is 20 and the length of one diagonal is 5, then the length of the other diagonal is _ _ _ _ _.

17. Diagonal AC and BD of rectangular ABCD intersect at point O,? AOD=60？ ，AB=23，AE？ BD, the vertical foot is E, then BD = _ _ _ _ _ _, BE = _ _ _ _ _.

18. In quadrilateral ABCD,? A=？ C, ab = 3, BC = 2, then CD = _ _ _ _ _

19. When the upper base of the trapezoid is 3 cm long and the lower base is 7 cm long, the area ratio of dividing these two parts by a diagonal line is _ _ _ _ _ _ _.

20. In trapezoidal ABCD, ABCD, the neutral line FE intersects with AD, AC, BD and BC at points E, G, H and F. If DC=5, AB= 1 1, then Eh = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Three. Problem solving (each question 10, ***40)

2 1. As shown in the figure, in trapezoidal ABCD, AD∨BC, AB=CD=AD,? C=60？ ，AE？ BD is at point E, F is the midpoint of CD, and DG is the height of trapezoidal ABCD.

(1) Verification: The quadrilateral AEFD is a parallelogram;

⑵ Let AE=x and quadrilateral area DEGF be y, and find the relationship between y and x.. ..

22. As shown in the figure, a rectangular ABCD is known.

(1) In the diagram, after being folded in half along the straight line where the diagonal BD is located, the point corresponding to point C is C? Draw with a ruler, keep clear traces of painting, and briefly describe the practice.

(2) Set C? The intersection of b and AD is e. If the area of △EBD is 13 of the whole rectangular area, what is it? Degree of CDB

23. As shown in the figure, in △ABC,? C=2？ B, D is a point on BC, and AD? AB, E is the midpoint of BD, connecting AE.

(1) Verification:? AEC=？ c；

⑵ Verification: BD = 2AC

⑶ If AE = 6.5 and AD = 5, what is the circumference of △ABE?

24. As shown in the figure, in △ABC, AB=AC,? A=90？ , BD split equally? ABC，CE？ E point BD

Verification: BD=2CE

Reference answer1:1.b2.c3.b4.a5.b6.b7.a8.B9.c10.d.

Second, 1 1.50? ,50? Or 80? ,20? 12. 1:3:2 13.20 14.24 15.43 16.53

17.4,3 18.433 19.3:7 20.5.5 3

3.2 1. Solution: (1) Omit (2) y = s 2 y = s =12ef? DG= 12？ 2x？ 3x = 3 x2(x & gt； 0) hours

22. Solution: (2) 30?

23. Solution: (3) Perimeter 25.

24. hint: extend ba and ce to point f and prove △ Abd △ ACF.