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As shown in the figure, in △ ABC, ab = AC, ad ⊥ BC, ad = AE, if ∠ bad = α, then ∠ EBC is equal to
In ∵ △ ABC, ad ⊥ BC, ab = AC, ∠ bad = α
∴∠DAC=∠BAD=α
∵AD=AE
∴∠ADE=1/2(180°-∠DAC)=90°-1/2α
∴∠EDC=90°-∠ADE=1/2α．
It is known that, as shown in Figure 2, e is the midpoint on the side of AC in △ ABC, ad ⊥ BC, ∠ EBC = 30 ° prove: ad = be
If we make a vertical line of BC through point E and intersect BC and F, then EF is parallel and equal to 1 / 2ad because e is the midpoint of AC and ad is the height of BC;
And because
As shown in the figure, △ ABC is an equilateral triangle, ad is the middle line, ad = AE, e is on AC, find the degree of ∠ EDC
The ∵ △ ABC is an equilateral triangle, ad is the middle line, ∵ ad ⊥ BC, ∵ CAD = 30 °, ∵ ad = AE, ∵ ade = ∠ AED = 180 °− ∠ CaD2 = 180 °− 30 ° 2 = 75 °, and ∵ EDC = ∠ ADC - ∠ ade = 90 ° - 75 ° = 15 °
As shown in the figure, △ ABC is an equilateral triangle, ad is the middle line, ad = AE, e is on AC, find the degree of ∠ EDC
The ∵ △ ABC is an equilateral triangle, ad is the middle line, ∵ ad ⊥ BC, ∵ CAD = 30 °, ∵ ad = AE, ∵ ade = ∠ AED = 180 °− ∠ CaD2 = 180 °− 30 ° 2 = 75 °, and ∵ EDC = ∠ ADC - ∠ ade = 90 ° - 75 ° = 15 °
RELATED INFORMATIONS
- 1. As shown in the figure, in the triangle ABC, BD bisector angles B and AE are perpendicular to BD and parallel to e and EF, and intersect AB with F
- 2. As shown in the figure, in the triangle ABC, ∠ ACB = 90 °, ad bisection ∠ BAC, de ⊥ AB is verified in E; the straight line ad is the vertical bisection of CE, seeking the help of the great God
- 3. As shown in the figure, in the triangle ABC, D is a point on the edge AB, and ad = AC, De is parallel to BC, CD bisection angle EDF proves that AF bisection CD
- 4. In triangle ABC, ad = 3bd, be = 2ec, AF = CF
- 5. As shown in the figure, △ ABC is an equilateral triangle, which is cut by a rectangle parallel to BC, and ab is cut into three equal parts. Then the area of the shadow part in the figure is () A. 19B. 29C. 13D. 49
- 6. (1) if EF = 5cm, then AB = --- (2) what's the difference between AF and de Please help··
- 7. In △ ABC, the angular bisectors AE and be of ∠ BAC and ∠ ABC intersect at point E, extend the circumscribed circle of AE intersecting △ ABC at point D, connect BD, CD and CE, and ∠ BDA = 60 ° ① prove that △ BDE is an equilateral triangle; ② guess what kind of quadrilateral bdce is if ∠ BDC = 120 ° and prove your guess; ③ under the condition of ②, when CE = 4, calculate the area of quadrilateral abdc
- 8. As shown in the figure, point I is the heart of △ ABC, the extension line of AI intersects with BC at point D, and intersects with the circumscribed circle of △ ABC at point E. verify EB = EC = EI
- 9. As shown in the figure, point I is the inner part of triangle ABC, AI intersects BC at point E, and intersection triangle ABC circumscribes circle at point D. prove (1dB = di (2id square = de * ad)
- 10. As shown in the figure, in △ ABC, ∠ C = 90 °, AC = BC, Da bisects ∠ cab and intersects BC at point D. can we determine a point E on AB so that the perimeter of △ BDE equals the length of AB? If yes, please point E and give proof; if not, please explain the reason
- 11. In the triangle ABC on the right, DC = 2bd, CE = 3aE, the area of the shadow is 20 square centimeters, and the area of the triangle ABC is______ Cm
- 12. An isosceles triangle is an axisymmetric figure. Its axis of symmetry is the middle line on the bottom edge of a and the high line on the bottom edge of B An isosceles triangle is an axisymmetric figure, and its axis of symmetry is A the center line on the bottom edge B the height on the bottom edge The line on which the bisector of C vertex is located D the line where the height of the waist is
- 13. The middle angle B of triangle ABC is 2 times angle c and ah is perpendicular to BC and h, BM = cm, ab = 2hm
- 14. Let p be a point in Δ ABC, and vector AP = (x-2y) vector AB + (Y-1) vector AC, then the value range of X is--- The value range of Y is-----
- 15. It is known that in △ ABC, ab = AC, D is the midpoint of BC side, P is any point on ad, PE ⊥ AB is in E, PF ⊥ AC is in F. try to explain: (1) PE = pf; (2) Pb = PC
- 16. In △ ABC, ab = AC, ad is the middle line, P is the upper point of AD, CF ∥ AB is made through point C, and the extension BP intersects AC at point E.1, which proves that BP = PC 2, and the square of BP = PE × pf?
- 17. In △ ABC, ad is an angular bisector, BP ⊥ ad is at point P, and ab = 5, BP = 2, AC = 9. It is proved that: ∠ ABC = 3 ∠ C
- 18. Let P = (a + C, b) and q = (B − a, C − a). If P ‖ Q, then the size of angle c is______ ．
- 19. It is known that the first n terms and Sn of sequence {an} satisfy Sn = 2an-1, and the arithmetic sequence {BN} satisfies B1 = A1, B4 = 7. Find the general term formula of sequence {an}, {BN}
- 20. The sum of the first n terms of the sequence {an} is Sn, and an is the median of Sn and 1. The sequence {BN} satisfies B1 = A1, B4 = S3 (1) Finding the general term formula of sequence {an}, {BN} (2) Let CN = 1 / BN * B (n + 1) and the sum of the first n terms of the sequence {CN} be TN. it is proved that 1 / 3 ≤ TN