1, under the following conditions, it can be judged that the quadrilateral ABCD is a parallelogram (d).
A.AB∨CD，AD = BCB. ∠B=∠C，∠A =∠D；
C.AB=AD，CB = CDD. AB=CD，AD=BC
2 Among the following propositions, the correct proposition is (D)
Two quadrangles with equal diagonals are rectangles.
B. A quadrilateral with two diagonal lines perpendicular to each other is a diamond.
A quadrilateral with two diagonal lines perpendicular to each other and equal is a square.
D. A quadrilateral with two diagonal lines bisecting each other is a parallelogram.
3. In the right triangle ABC, ∠ ACB = 90, ∠ A = 30 MAC = 3cm, then the length of the median line on the side of AB is (A).
A. 1 cm B. 2cm C.1.5cm D. The number of roots is 3cm.
4. If the difference between the two bottoms of the isosceles trapezoid is 12cm and the height is 6cm, then the acute angle of the isosceles trapezoid is (b).
A 30 B 45 C 60 D 75
5. In the right triangle ABC, ∠ ACB=90, ∠ A=30, and AC= 3cm, then the center line on the side of AB is (A).
A 1cm B 2cm C 1.5cm D radical 3cm
6. The length of the high line on one side of an equilateral triangle is 2 numbers 3cm, so the length of the middle line of this equilateral triangle is (C).
A 3 cm, a 2.5 cm, a 2 cm and a 4 cm.
7, the following judgment is correct (C)
A quadrilateral with diagonal lines perpendicular to each other is a diamond.
An equilateral quadrilateral is an isosceles trapezoid.
A quadrilateral with four equal sides and a right angle is a square.
Two quadrangles with equal diagonal lines and perpendicular to each other are squares.
Second, fill in the blanks
If the diagonal lengths of 1 and the diamond are 6 and 8 respectively, then the circumference of this diamond is _20__.
2. The quadrilateral obtained by connecting the midpoints of each side of the quadrilateral in turn with equal diagonal lines is _ diamond _ _.
3. If the diagonal length of a square is 2 cm, the side length is 2 cm.
Third, solve the problem (the picture is wrong)
Solution: Let AB be X, then BC is (1 1-X). When BC crosses A, the vertical line intersects BC at point E.
Because ∠ b = 30
So AE= half x, that is:
Half x * (11-x) =15.
x？ - 1 1X+30=0
(X-5)(X-6)=0, so AB=5 BC=6 or
X=5 or 6 BC=5 AB=6.