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As shown in the figure, in △ ABC, ab = AC, D is a point on the edge of BC, with AB and BD as adjacent sides, make parallelogram ABDE and connect AD and EC
It is proved that: ∵ AB = AC, ∵ ABC = ACB, ∵ quadrilateral ABDE is parallelogram, ∵ ab ∥ De, ab = De, ∵ ABC = EDC, ∵ ACD = EDC, ∵ AB = AC, ab = De, ≌ AC = de. in △ ADC and △ ECD, AC = De, ACD = edccd = DC, ≌ ADC ≌ ECD (SAS)
In △ ABC, BD and CE are the midlines on the edges AC and ab. BD and CE intersect at point o. ① what is the relationship between the length of Bo and OD? Please prove. 2. Does the center line on the side of BC necessarily cross point o? Why?
① The reason is as follows: connecting de. ∵ BD and CE is the midline on the side AC and AB, ∵ de ∥ BC, de = 12bc. ∵ ode ≓ OBC, ∥ obod = BCDE, that is, Bo = 2od. ② the midline on the side BC must pass through point O. the reason is: making the midline AF on the side BC, intersecting BD to m, connecting DF, ∵ BD and AF are the midline on the side AC and BC, ∥ DF ∥ Ba, DF = 12ba. ∥ MDF ∥ MBA, ∥ dmbm = FMAM = dfab = 1 2, that is, BD = 3DM, ∵ Bo = 23bd, ∵ O and M coincide, that is, the middle line on the edge of BC must pass through point o
As shown in the figure, in the triangle ABC, BD and CE are the midlines on the sides AC and ab respectively. What is the relationship between the intersection of BD and CE and the length of Bo and OD?
(parallelogram rectangle diamond Square)
A trapezoidal decorative board, upper bottom 6 decimeters, lower bottom 10 decimeters, 1 meter high, both sides should be painted, painted area is () square decimeters
1 m = 10 decimeters;
Area of two sides
=2 × (upper bottom + lower bottom) × height △ 2
=(6+10)×10
=160 (square decimeter)
The shape of an iron plate is shown in the figure. Paint the two sides of the iron plate. What is the area of the paint? (unit: decimeter)
8 × 8 + (4 + 2 + 4 + 2) × (10-8) △ 2 = 64 + 12 × 2 △ 2 = 64 + 12 = 76 (square decimeter) 76 × 2 = 152 (square decimeter) a: the area of painting is 152 square decimeter
As shown in the picture, use a round iron plate with an area of 54 square meters to cut out 7 campus row iron plates of the same size, and the remaining iron plate surface
As shown in the figure, use a round iron plate with an area of 54 square meters to cut seven small round iron plates of the same size. What is the area of the remaining iron plate?
Direct use of 54 / 7 is about 7.714
Then 54-7 * 7 = 5 square meters
How much is the shadow area after cutting a circle on a square iron plate with a side length of 30 cm
Square area = 30 * 30 = 900 square centimeter
Circular area = 3.14 * 15 * 15 = 706.5 square centimeter
Shadow area = square area - circle area = 193.5 square centimeter
To cut a square iron plate with an area of 36m2, what is its side length
Because:
36=6*6
So the side length is 6 meters
Or:
Root 36 = 6M
On the circular iron plate with a radius of 20cm, if you want to cut a square iron plate with the largest area as a machine part, find the side length of the largest square（
Cut a square iron plate with the largest area from a circular iron plate with a radius of 20cm for machine parts, and calculate the side length of the largest square. (the error is not more than 0.1cm)
The diagonal of a square is equal to the diameter of a circle
Square area: 1 / 2 * 40 * 40 = 800
Square area = side length * side length = 800, side length = 28.3
RELATED INFORMATIONS
- 1. In the triangle ABC, BD and CE are the midlines on the sides AC and ab. BD and CE intersect at the point O. what is the relationship between the length of Bo and OD? For detailed explanation, do not run to copy, correct answer, I can add 20-50 points to see the picture
- 2. As shown in the figure, in △ ABC, the bisector of ∠ ABC and ∠ ACB intersects at point I. according to the following conditions, calculate the degree of ∠ BIC 1. If ∠ ABC = 60 °, ACB = 70 °, then ∠ BIC=____ 2. If ∠ ABC + ∠ ACB = 130 °, then ∠ BIC=____ 3. If ∠ a = 50 °, then BIC=____ 4. From the above calculation, what is the quantitative relationship between ∠ A and ∠ BIC? Please prove it
- 3. If the lengths of the two right sides of a right triangle are 3 and 4 respectively, what is the radius of its inscribed circle
- 4. If the inner and outer centers of a triangle coincide, then the triangle is, and the ratio of the radius of its circumscribed circle to the radius of its inscribed circle is
- 5. Given that the circle O is the circumscribed circle of triangle ABC, and the side length is 6, the radius of circle O is calculated
- 6. If the hypotenuse BC of the right triangle ABC is 1 and the circle O is the inscribed circle of the triangle ABC, then the maximum radius of the circle O is 0
- 7. If one side of a triangle is (2a-b) cm long, the second side is (a + b) cm longer than the first side, and the third side is 2 times less than the first side by B cm (1) What's the circumference of this triangle in centimeters? (2) If the triangle is isosceles triangle and the second and third sides are equal, the perimeter of the triangle when B = 2 is obtained
- 8. The first side of a triangle becomes {2a-b} cm, the second side is {a = 2B} cm longer than the first side, and the third side is less than 2 times of the first side by B. calculate the perimeter
- 9. Given that the perimeter of the triangle is 5a-b, the length of the first side is 3A + 2B, and the length of the second side is twice that of the first side, which is a-2b + 2 less than that of the first side, the length of the third side can be obtained
- 10. Xiaowan drew four points on the paper. If the four points were connected to form a figure, how many triangles would there be in the figure?
- 11. As shown in the figure, in the triangle ABC, D, e and F are the midpoint of three sides BC, AC and ab respectively. It is proved that the quadrilateral defb is a parallelogram
- 12. (1 / 2) we know that the two high BD and CE of the acute triangle ABC intersect at O, and ob = OC, and prove that: (1) the triangle ABC is isosceles triangle (1 / 2) it is known that the two high BD and CE of the acute triangle ABC intersect at the point O, and ob = OC. It is proved that: (1) the triangle ABC is an isosceles triangle. (2) whether o is at the angular plane of the angle ABC is determined
- 13. What is the area of a right triangle when the length of two right sides of a right triangle is two prime numbers and the sum is 18?
- 14. In an isosceles triangle with a circumference of 10 cm, the length of the bottom edge is x (CM), and the length of the waist is y (CM). Write out the analytic expression of the function of Y with respect to X and the definition domain of the function
- 15. In the triangle ABC, ab = AC, BD is the center line on the side of AC. BD divides the circumference of ABC into two parts: 36 and 63, and calculates the length of BC Let the waist length of this isosceles triangle be a and the bottom length be B be A+A/2=36 B+A/2=63 A = 24, B = 51 is obviously not true Or a + A / 2 = 63 B + A / 2 = 36 A=42 B=15 establish So BC = 15 Why is BD not included in the weekly schedule
- 16. As shown in the figure, in the equilateral triangle ABC, D and E are the points on the sides of AB and BC respectively, ad = be, AE intersects CD at point F, Ag ⊥ CD at point G, if Ag = 2, then the value of AF is () A. 52B. 32C. 34D. 433
- 17. As shown in the figure, in the triangle ABC, ab = AC = a, take BC as the edge, make an equilateral triangle outward, and find the maximum value of AD
- 18. As shown in the figure, in the triangle ABC, the angle ABC = 45 degrees, and H is the intersection point of the higher he be
- 19. If the positions of the corresponding points of real numbers a, B and C on the number axis are shown in the figure, the absolute value of B + 2 + the absolute value of a-C is obtained A is a positive number, B, C is a negative number, B is greater than C
- 20. As shown in the figure, in △ ABC, ab = AC, ∠ a = 50 ° and BD is the bisector of ∠ ABC, then ∠ BDC=______ Degree