Given a + B + C = 0, ABC = - 15, find AA (B + C) + BB (a + C) + CC (a + b)

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• 1. As shown in the figure, in the isosceles right angle △ ABC, ∠ ABC = 90 °, point D is on AC, and △ CBE is obtained after △ abd is rotated 90 ° clockwise around vertex B. (1) calculate the degree of ∠ DCE; (2) when AB = 4, ad: DC = 1:3, calculate the length of de
• 2. If the right angle vertex C of RT △ ABC is in plane a, the hypotenuse ab ‖ a, and the distance between AB and a is root 6, the projective points of a and B in a are A1 and B1 respectively, and A1C = 3, B1C = 4, then ∠ a1cb1=
• 3. Ad is the height of triangle ABC, de ⊥ AB, DF ⊥ AC, and the vertical foot is a and e respectively. Try to judge the size of ∠ ADF and ∠ AEF and explain the reason Using similar triangle to solve the problem
• 4. Ad is the bisector of triangle ABC, De is parallel to AC, de intersects AB with E, DF is parallel to AB, DF intersects AC with F. what is the relationship between angle EDA and angle ADF?
• 5. In a right triangle ABC, angle a is a right angle, point D is the midpoint of BC, e is on AB, f is on AC, De is perpendicular to DF, and we prove that EF square = be square + CF square
• 6. In △ ABC, ab = AC, D is the midpoint of BC, e and F are on AB and AC respectively, and △ DEF is an equilateral triangle
• 7. As shown in the figure, △ ABC is a right triangle, ∠ ACB = 90, ad is the bisector of ∠ BAC, de ⊥ AB, BC = 8, CD = 3, the length of 1.be, 2. The area of △ ABC
• 8. It is known that: as shown in the figure, in △ ABC, the bisector am of ∠ C = 90 °, BAC = 60 ° is 15cm, and the length of BC is calculated
• 9. As shown in the figure, it is known that △ ABC is an isosceles right triangle, ∠ BAC = 90 °, be is the bisector of ∠ ABC, de ⊥ BC, and the perpendicular foot is d. (1) please write all isosceles triangles in the figure; (2) please judge whether AD is perpendicular to be? (3) if BC = 10, find the length of AB + AE
• 10. ABC is isosceles right triangle, ∠ BAC = 90 °, be is angle horizontal line, ed ⊥ BC, prove ad vertical be
• 11. Ask math question AA + BB + CC = ABC What are the ABC numbers?
• 12. As shown in the figure, △ ABC rotates counterclockwise to the position of △ ab ′ C ′ so that AC bisects BB ′
• 13. It is known that △ ABC is all equal to △ def, the perimeter of △ ABC is 32, ab = 8, BC = 12, then CA =?, de =? EF =?
• 14. If the triangle ABC is equal to the triangle def, the circumference of the triangle ABC is 70cm, De is 30cm, DF is 25cm, and the angle B is 25cm
• 15. In △ ABC, DB and DC divide ∠ ABC and ∠ ACB equally, and intersect at point D, BG and CG divide ∠ CBE and ∠ BCF equally, and intersect at point G Verification: ∠ DBG = 90 degrees
• 16. As shown in the figure, △ ABC is an equilateral triangle, D is the midpoint of AB, de ⊥ AC is at e, EF ∥ AB intersects BC at F, CE = 3cm Find the circumference of (1) △ ABC; (2) Area of trapezoidal bdef
• 17. The triangle ABC, CE is perpendicular to AB, e, BF is perpendicular to AC, F, M is the midpoint of BC, EF is 5cm long, BC is 8cm long, find the perimeter of triangle EFM
• 18. As shown in the figure, D is the midpoint of BC, the length of ad is three times that of AE, the length of EF is three times that of BF, the area of triangle AEF is 18 square centimeters, and the area of triangle ABC is 18 square centimeters What's the square centimeter?
• 19. The area of △ AEF is equal to the area of trapezoidal EFBC
• 20. In the triangle ABC, the bisector of angle ACB intersects AB at e, EF parallels BC, intersects AC at F, and the bisector of the outer angle of angle ACB intersects G Try to judge the shape of the triangle EFC and explain your reason