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As shown in Figure 1, fold the △ ABC paper along De, so that point a falls at the position of point a 'in the quadrilateral bced. Through calculation, we know that: 2 ∠ a = ∠ 1 + ∠ 2 (1) If the △ ABC paper is folded along the de so that the point a falls on the position of the outer point a 'of the quadrilateral bced, as shown in Fig. 2, what is the relationship between ∠ A and ∠ 1, 2? Why? Please explain the reason. (2) if the quadrilateral ABCD is folded along EF so that the points a and d fall on the positions of a 'and d' inside the quadrilateral BCFE, as shown in Figure 3, can you find out the relationship between ∠ a, ∠ D, ∠ 1 and ∠ 2? (write the relation directly)
(1) Connect AA ′, ∵ ∠ 2 = ∠ a ′ AE + ∠ AA ′ e, ∠ 1 = ∠ a ′ AD + ∠ AA ′ D; ∠ 1 - ∠ 2 = 2 ∠ a; (2) according to the nature of graph folding, it can be known that ∠ 1 = 180 ° - 2 ∠ AEF, ∠ 2 = 180 ° - 2 ∠ DFE, adding the two formulas, it can be concluded that ∠ 1 + ∠ 2 = 360 ° - 2 (∠ AEF + ∠ DFE), that is ∠ 1 + ∠ 2 = 360 ° - 2 (360
As shown in the figure, when △ ABC is folded along De, when point a falls inside the quadrilateral bced, there is a quantitative relationship between ∠ A and ∠ 1 + 2, which remains unchanged,
Please try to find the law. What is the law you found? Explain the correctness of the law you found
http://zhidao.baidu.com/question/101127983.html
Here's the picture
Please change figure C and figure a, and then change with figure B, that is, where a is at C, where C is at B, and where B is at a
∠1=180°-2∠DEF
∠2=180°-2∠EDF
∠DEF+∠EDF=180-∠F
∴∠1+∠2=360°-2(∠DEF+∠EDF)=360°-2(180°-∠F)=2∠F=2∠A
RELATED INFORMATIONS
- 1. (1) As shown in Figure 1, fold the △ ABC paper along de so that point a falls at the position of point a 'inside the quadrilateral bced, and try to explain that 2 ∠ a = ∠ 1 + ∠ 2; (2) as shown in Figure 2, if the △ ABC paper is folded along de so that point a falls at the position of point a' outside the quadrilateral bced, then the equivalent relationship between ∠ A and ∠ 1, ∠ 2 is______ (no need to explain the reason); (3) as shown in Figure 3, if the quadrilateral ABCD is folded along EF, so that points a and d fall on the positions of internal points a ′, D ′ of quadrilateral BCFE, please explore the quantitative relationship between ∠ a, D, 1 and 2 at this time, write down the conclusion you found and explain the reason
- 2. As shown in the figure, D and E are the points on △ ABC sides AB and AC respectively, de ‖ BC. If ad = BD, find the ratio of the area of triangle ade to the area of trapezoid bced
- 3. It is known that a (0, - 4), B (- 2,0) C (3,0) are the three vertices of △ ABC. A straight line L passing through the coordinate origin o intersects the line segment AB at point D, and the bisector of ∠ ADO and ∠ ABO intersects at point M?
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- 7. As shown in the figure, in △ ABC, AE bisects ∠ BAC, ∠ C ＞ B, f is the point above AE, and FD ⊥ BC is at point D. try to deduce the relationship between ∠ EFD, ∠ B and ∠ C When the point F is on the extension line of AE, as shown in Figure 2, the other conditions remain unchanged. Is the conclusion you deduced in question 1 still valid? Please give reasons.
- 8. As shown in the figure, in △ ABC, de and FG are the vertical bisectors of AB and AC, respectively. If BC = 10, what is the perimeter of △ ADF?
- 9. In triangle ABC, we know EF / / BC, | BC | = radical 2 | BF |. It is proved that the area of triangle AEF is equal to the area of trapezoidal ebcf
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- 12. The side length of equilateral triangle ABC is a, and the square defg is inscribed with △ ABC, D, E on AB, AC, G, f on BC respectively. Find the side length of square defg
- 13. If AB is 1:4 to de, the sum of the circumference of the equilateral triangle ABC and the square defg is 76 cm, what is the circumference of the triangle? AB is one side of an equilateral triangle, De is one side of a square,
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- 15. In △ ABC, ab = AC, ad ⊥ BC is at point D, and points E and F are the midpoint of AB and AC sides respectively. When △ ABC satisfies what conditions, the quadrilateral AEDF is a square
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