As shown in the figure, ABC is an equilateral triangle, BD is the middle line, extend BC to e, so that CE = CD
It is proved that: ∵ ABC is an equilateral triangle, BD is the middle line, ∵ ABC = ∠ ACB = 60 °, DBC = 30 ° (isosceles triangle three lines in one), and ∵ CE = CD, ∵ CDE = ∠ CED. And ∵ BCD = ∠ CDE + ∠ CED, ∵ CDE = ∠ CED = 12 ∠ BCD = 30 °. ∵ DBC = ∠ Dec. ∵ DB = de (equiangular to equilateral)
RELATED INFORMATIONS
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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.
- 7. 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
- 8. In △ ABC, if Sina: SINB: sinc = 2:3:4, then the cosine value of the largest angle=______ .
- 9. Finding cosine C in triangle ABC with a = 3, B = 5 and C = 7
- 10. In △ ABC, if a = 7, B = 8, COSC = 1314, then the cosine of the largest angle is () A. −15B. −16C. −17D. −18
- 11. a. B and C are the three sides of triangle ABC. It is proved that a ^ 2 = B (B + C) is a = 2B Please give the proof of sufficiency and necessity
- 12. It is known that a, B and C are the three sides of triangle ABC, and the square of a + the square of 2B + the square of C is equal to 2B (a + C) It is known that a, B and C are the three sides of triangle ABC, and the square of a + the square of 2B + the square of C is equal to 2B (a + C). Try to judge the shape of triangle ABC and explain the reason
- 13. Let a, B, C be the three sides of triangle ABC, and (C-B) x2 + 2 (B-A) x + A-B = 0, with two equal real roots, prove that triangle ABC is isosceles triangle
- 14. Factorization of A2 + B2 + c2-2c-2ab-1 Factorization a ^ 2 + B ^ 2 + C ^ 2-2c-2ab + 1,
- 15. Given A2 + B2 = C2 + D2 = 1, find the value of (AC BD) 2 + (AD + BC) 2 Please write the process in detail, I wait online, please hurry up! Thank you!
- 16. What is the volume of the cuboid when the area of the three faces passing through the same vertex of the cuboid is 2, 4 and 8 There should be formula and written narration. Thank you
- 17. Put two cuboids that are 8 cm long, 6 cm long and 5 cm high together to form a large cuboid. How many square centimeters is the maximum surface area of this large cuboid?
- 18. The cuboid is 12 cm long and 8 cm high. The sum of the areas of the two sides of the shadow is 180 square cm. What is the cuboid's volume in cubic cm
- 19. The area of three sides of a cuboid is 6, 8 and 12 respectively. What is the volume of this cuboid?
- 20. The length, width and height of a cuboid are a, B and C meters respectively. If the height increases by 2 meters, and the length and width remain unchanged, the volume of the new cuboid will increase () A. A×B×(C+2)B. 2ABC. 2ABC