Known: as shown in the figure, in △ ABC, if ∠ A is an acute angle, points D and E are on AB and AC respectively, and ∠ DCB = ∠ EBC = 12 ∠ A. verification: BD = CE

Proof 1: as shown in Figure 1, make CG ⊥ be at point G, BF ⊥ CD at point F. in ⊥ CG ⊥ be, BF ⊥ CD, ≠ f = ∠ CGB = 90 °, in ⊥ BCF and ⊥ CBG, ⊥ f = ∠ CGB = 90 ⊥ DCB = ∠ ebcbc, ≌ BCF ≌ CBG (AAS), ⊥ BF = CG, ⊥ BDF = ∠ Abe + ∠ EBC +} D

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1. Known: as shown in the figure, in △ ABC, if ∠ A is an acute angle, points D and E are on AB and AC respectively, and ∠ DCB = ∠ EBC = 12 ∠ A. verification: BD = CE
2. In △ ABC, the points o and E are on AB and AC respectively, ∠ DCB = ∠ EBC = 1,2 ∠ a, be and CD intersect at point O to prove BD = CE The following first answer is not for junior high school students, the second answer is wrong, also can't be used, hope someone continue to give guidance.
3. In △ ABC, if sin B = 2sinacosc and the cosine of the minimum angle is 3 / 4, (1) judge the shape of triangle ABC, (2) find the maximum angle of ABC
4. In △ ABC, if Sina: SINB: sinc = 2:3:4, then the cosine value of the largest angle=______ ．
5. Finding cosine C in triangle ABC with a = 3, B = 5 and C = 7
6. In △ ABC, if a = 7, B = 8, COSC = 1314, then the cosine of the largest angle is () A. −15B. −16C. −17D. −18
7. In the triangle ABC, the cosine of ∠ A is 5 / 13, and the cosine of ∠ B is 4 / 5?
8. In △ ABC, if a = 7, B = 8, COSC = 1314, then the cosine of the largest angle is () A. −15B. −16C. −17D. −18
9. In the triangle ABC, if a: B: C = 7:8:13, then the cosine of the largest inner angle in the triangle is
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11. In the triangle ABC, the points D and E are on AB and AC, and the angle EBC = angle DCB = I / 2 angle a, BD = CE is proved
12. Known: as shown in the figure, in △ ABC, if ∠ A is an acute angle, points D and E are on AB and AC respectively, and ∠ DCB = ∠ EBC = 12 ∠ A. verification: BD = CE
13. In known triangle ABC, angle ACB is equal to 90 degrees, AC is equal to BC, ad is vertical to CE, be is vertical to CE, D and E are perpendicular feet
14. As shown in the figure, ABC is an equilateral triangle, BD is the middle line, extend BC to e, so that CE = CD
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