In △ ABC, ad bisects ∠ BAC, intersects BC with D, EF ‖ ad, intersects AC with E, intersects the extension of BA with F. it is proved that △ AEF is an isosceles triangle
It is proved that: ∵ EF ‖ ad, ∵ f = ∵ bad, ∵ AEF = ∵ DAC. ∵ ad bisects ∵ BAC, ∵ bad = ∵ DAC, ∵ f = ∵ AEF, ∵ AE = AF, i.e. △ AEF is isosceles triangle
RELATED INFORMATIONS
- 1. As shown in the figure, in △ ABC, e is a point on the edge of BC, EF is perpendicular to BC, intersects BA at D, intersects the extension line of Ca at F, if ad = AF, is △ ABC an isosceles triangle
- 2. The inscribed circle O of the right triangle ABC, the hypotenuse AB at point D, the tangent BC at point F, and the intersection AC of the extension line of Bo at point E
- 3. As shown in the figure, the inscribed circle O of RT △ ABC cuts the hypotenuse AB to D, cuts BC to F, and the extension line AC of Bo intersects at point E Prove Bo * BC = BD * be
- 4. In the regular triangular prism abc-a1b1c1, ab = 2, Aa1 = 1, find the distance from point a to plane a1bc
- 5. In the triangular prism abc-a1b1c1, ab = AC = 2aa1, ∠ baa1 = ∠ caa1 = 60 °, D and E are the midpoint of AB and A1C respectively
- 6. In the straight triangular prism abc-a1b1c1, ∠ ACB = 90 ° Aa1 = AC = a, then the distance from point a to plane a1bc is?
- 7. In the regular triangular prism abc-a1b1c1, if AB = 2 and a & nbsp; A1 = 1, then the distance from point a to plane a1bc is () A. 34B. 32C. 334D. 3
- 8. It is known that each edge length of oblique triangular prism abc-a1b1c1 is 1, and the angle a1ab = angle a1ac = 60 degrees How to prove bcc1b1 as a square
- 9. As shown in the figure, it is known that all edges of the regular triangular prism abc-a1b1c1 are equal in length, and D is the midpoint of a1c1, then the sine value of the angle between the straight line AD and the plane b1dc is______ .
- 10. In the regular triangular prism abc-a1b1c1, if all edges are equal in length, then the tangent of the angle between the straight line CB1 and the plane aa1b1b is () A. Root 15 / 3 B. root 15 / 5 C. root 5 / 5 d. root 2
- 11. )As shown in the figure, it is known that ∠ ABC = 60 °, ACB = 50 °, Bi bisection ∠ ABC, CI bisection ∠ ACB, Bi and CI intersection at I, passing through point I as De, (1) calculate the degree of ∠ BIC (2) Guess the quantitative relationship among BD, CE and De, and explain the reason
- 12. In △ ABC, Bi bisection ∠ ABC, CI bisection ∠ ACB, be, CE are bisection lines of external angle, if ∠ a = 50 °, then ∠ I =? ° ∠ Ube =? ±
- 13. If a, B and C are three sides of △ ABC, the result of simplifying | a-b-c | + | b-c-a | + | C-A-B |, is () A. -a-b-cB. a+b+cC. a+b-cD. a-b+c
- 14. Note that the lengths of the three sides of the triangle ABC are a, B, C. simplify the algebraic formula ia-b-ci + ia-b + CI + Ia + b-ci
- 15. AAA+BBB-CCC=?DDD A
- 16. AAA+BBB+CCC=CBBC What does a stand for? What does B stand for
- 17. AAA + BBB + CCC = CBBC question; a =? B =? C =?
- 18. Three sides a, B, C of triangle ABC satisfy AA + BB + CC + 338 = 10A + 24B + 26c, and the area of triangle ABC is calculated
- 19. The triangle ABC must satisfy π / 3
- 20. Three sides ABC of triangle, find aa-bb-cc-2ab < 0