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)

As shown in the figure, △ ABC, ab = AC, extend BC to D, make CD = BC, point E on edge AC, make ▱ cdfe with CE and CD as the adjacent edge, cross point C as CG ∥ AB with point G, connect BG, de. (1) ∠ ACB and ∠ GCD. What is the quantitative relationship? (2) verification: △ BCG ≌ △ DCE

(1) The reasons are as follows: ∵ AB = AC, ∵ ABC = ∵ ACB ∵ CG ∥ AB, ∵ ABC = ∵ GCD, ∵ ACB = ∵ GCD. (2) it is proved that ∵ quadrilateral cdfe is a parallelogram, ∥ EF ∥ CD.

RELATED INFORMATIONS

1. It is known that the midpoint D.E of triangle ABC is a point on AB and AC respectively, and satisfies AD / DB = AE / EC = 1 / 2. How many times is BC equal to de? (not isosceles triangle) the process should be detailed
2. In △ ABC, Ba = BC, ∠ ABC = 45 °, ad is the height on the edge of BC, e is a point on ad, ed = CD, connecting EC
3. D is the midpoint of the side BC of the triangle ABC, e is a point on the side AC, and the extension line of Ba and de intersects at the point F
4. It is known that: as shown in the figure, points B, C and D are on the same straight line, ∠ ACB = ∠ ECD = 60 °, AC = BC, EC = DC. Connect be and ad, intersect AC and CE at points m and N respectively. Verify: (1) ACD ≌ BCE; (2) cm = CN
5. If the perimeter of a right triangle is 1, find its maximum area Using inequality
6. Let lgx lgY = a, then lg5x3-lg5y3?
7. We know that f (x) = lgx (x > = 1), - lgx (0)
8. What is the minimum value of the function y = LG (x / 3) LG (x / 12) when x is Urgent!
9. The function f (x) = AX2 + 4x-3, when x belongs to [0,2], the maximum value is obtained at x = 2, and the value of a is obtained
10. It is known that a certain railway bridge is 500m long. Now a train passes through the bridge at a constant speed. It takes 30s for the train to get on the bridge and finish it. The time for the whole train to be completely on the bridge is 20s. How long is the train?
11. 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
12. As shown in the figure, in △ ABC, the angle a = 60 ° and the circle O with BC as diameter intersects with AB and AC at points D and e respectively. Try to judge the shape of △ deo and prove it
13. In RT triangle ABC, angle ACB is equal to 90 degrees, angle a = 30 degrees, BD is the bisector of triangle ABC, De is perpendicular to point E 1, In RT triangle ABC, angle ACB is equal to 90 degrees, angle a = 30 degrees, BD is the bisector of triangle ABC, De is perpendicular to point E Q: connect EC and prove that the triangle EBC is an equilateral triangle
14. It is known that in △ ABC, ab = AC = 13, BC = 10, then the radius of the inscribed circle of △ ABC is () A. 103B. 125C. 2D. 3
15. Triangle ABC, angle bisector of angle a intersects with D, BD = 3, DC = 4, find the inscribed circle radius of triangle ABC
16. As shown in the figure, △ ABC, ab = AC, points D, e and F are on edges BC, AB and AC respectively, and BD = CF, ∠ EDF = ∠ B. is there a triangle congruent with △ BDE in the figure? And explain the reason
17. In △ ABC, a, B and C are the opposite sides of angles a, B and C respectively, a = 60 ° and (b-2c) / ACOS (60 ° + C)=
18. In the acute triangle ABC, AB > AC, CD and be are the heights on the sides of AB and AC respectively. The extension line of De and BC is called t, and the vertical line of BC crossed by D, BC crossed by F, It is proved that f, G and T are collinear
19. In the acute triangle ABC, AB equals 14, BC equals 14, the area of triangle ABC is 84, find the value of Tanc and sinc I have worked it out, but the result is too complicated. If you want to verify it, please give the result
20. In the triangle ABC, D and E are close to the trisection point of a and B respectively. How many times is the area of triangle ABC?