As shown in the figure, in RT △ ABC, ∠ ACB = 90 °, point D is a point on the hypotenuse AB, make ∠ CDE = ∠ a, pass through point C, make CE ⊥ CD, cross De to e, connect be Verification: ab ⊥ be

According to the judgment of similar triangles, △ BCE ∽ ACD is obtained. According to the known and similar triangles' corresponding angles are equal, the conclusion can be obtained. ∵ CE ⊥ CD, ∵ DCE = ∠ ACB = 90 ° and ∵ CDE = ∠ a ∽ DCE ∽ ACB, ∵ CE / CB = CD / Ca, ∵ CE / CD = CB / Ca, ∵ DCE = ∠ ACB = 90 ° and ∵ BCE = ∠

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1. In △ ABC, ab = BC, ∠ a = ∠ C = 45 ° rotate △ ABC clockwise around point B by an angle α (0 ＜ α ＜ 90 °) and △ MBN, BM intersect AC with point E, Mn intersect AC, BC with D and f respectively (1) When α =? EM is the longest; (2) Observe and guess the quantitative relationship between EM and FC in the process of rotation, and explain the reason There should be an answer before 6:30 tomorrow, otherwise it will be invalid
2. As shown in the figure, ab = BC, ∠ ABC = 90 ° in △ ABC, and △ ABC rotates clockwise around point B to △ a1bc1, and the rotation angle is α, 0 °
3. As shown in the figure, rotate the right angle triangle ABC (where ∠ ABC = 60 °) clockwise around point B to the position of a1bc1, so that points a, B and C1 are on the same straight line. If the length of AB is 10, then the distance from point a to point A1 is equal to the distance______ (results π reserved)
4. As shown in the figure, in the acute angle △ ABC, ab = 4, BC = 5, ∠ ACB = 45 °, rotate △ ABC counterclockwise around point B to obtain △ a1bc1. (1) as shown in Figure 1, when point C1 is on the extension line of line Ca, calculate the degree of ∠ cc1a1; (2) as shown in Figure 2, connect Aa1 and CC1. If the area of △ aba1 is 4, calculate the area of △ cbc1
5. As shown in the figure, ab = AC, ∠ BAC = 120 ° in △ ABC, ad ⊥ AC intersects BC at point D, and BC = 3aD
6. As shown in the figure, ab = AC, ∠ BAC = 120 ° in △ ABC, ad ⊥ AC intersects BC at point D, and BC = 3aD
7. As shown in the figure, ab = AC, ∠ BAC = 120 ° in △ ABC, ad ⊥ AC intersects BC at point D, and BC = 3aD
8. As shown in the figure, ab = AC, ∠ BAC = 120 ° in △ ABC, ad ⊥ AC intersects BC at point D, and BC = 3aD
9. As shown in the figure, ab = AC, ∠ BAC = 120 ° in △ ABC, ad ⊥ AC intersects BC at point D, and BC = 3aD
10. It is known that AC = 6BC = 8 in RT △ ABC, and Tan ∠ CDE can be obtained by turning an acute angle of it It is known that in RT △ ABC, ∠ C = 90 °, AC = 6, BC = 8, fold an acute angle so that the vertex of the acute angle falls at the midpoint D of the opposite side, and the crease intersects the other right edge at e and the oblique edge at F. the value of Tan ∠ CDE is obtained
11. In RT △ ABC, CD is the bisector of BCE. BCE = 60 °∠ 3 = ∠ 4. Describe the relationship between CB and CE. What's your conjecture? And prove it Note that it's in the RT triangle
12. In RT △ ABC, ∠ C is equal to 90 degree CD.CE If ∠ A is equal to 30 °, try to judge the shape of ∠ BCE Geometric steps, is an equilateral triangle
13. As shown in the figure, in the triangle ABC, the angle BAC = 90 ° and BD is the bisector of the angle ABC. The extension line of BD is perpendicular to the line passing through point C and E, and the extension line of CE intersecting Ba is F. the proof is: BD = 2ce Please help me
14. As shown in the figure, in the triangle ABC, ab = BC, ad is the middle line on BC, extend BC to point E, make CE = BC, prove: AE = 2ad
15. As shown in the figure, ad is the middle line of △ ABC, point E is on the extension line of BC, CE = AB, ∠ BAC = ∠ BCA, verification: AE = 2ad
16. As shown in the figure, in the triangle ABC, angle a is equal to 60 degrees, angle B is equal to 75 degrees, ab = 4cm, find C of BC
17. As shown in the figure, in △ ABC, it is known that ∠ DBC = 60 ° AC ＞ BC, and △ ABC ′, △ BCA ′, △ cab ′ are equilateral triangles outside △ ABC shape, and point D is on AC, and BC = DC (1) prove: △ C ′ BD ≌ Δ B ′ DC; (2) prove: △ AC ′ D ≌ Δ DB ′ a
18. As shown in the figure, it is known that in △ ABC, ab = AC, the vertical bisector De of AB intersects AC at point E, and the vertical bisector of CE just passes through point B and intersects AC at point F. the degree of ∠ A is calculated
19. As shown in the figure, it is known that in △ ABC, ab = AC, the vertical bisector De of AB intersects AC at point E, and the vertical bisector of CE just passes through point B and intersects AC at point F. the degree of ∠ A is calculated
20. As shown in the figure, it is known that in △ ABC, ab = AC, the vertical bisector De of AB intersects AC at point E, the perpendicular foot is D, and the vertical bisector of CE is just right When passing through point B, the perpendicular foot is f, then the degree of ∠ A is—— I'm in a hurry. I still have a lot of homework. There are only a few questions left Help, I'm too lazy to do it. You should draw it out. The answer is 36 degrees. How can you figure out what it is like, give it to you, and hope you can give it awesome.