As shown in Figure 6, in △ ABC, the vertical bisector Mn of ∠ a = 105 ° AC intersects at point n, AC intersects at point m, and ab + BN = BC,

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• 1. In the triangle ABC, the angle BAC = 135 degrees, Fe and GH are the vertical bisectors on both sides of AB and AC respectively, and intersect with BC at points E and G to find the degree of angle EAG
• 2. As shown in the figure, in △ ABC, ab = AC, ∠ B = 30 °, the vertical bisector EF of AB intersects AB at point E, BC at point F, EF = 2, then the length of BC is______ ．
• 3. In △ ABC, ab = AC, ∠ B = 30 °, the vertical bisector EF of AB intersects AB at point E and BC at point F. if CF = 6 cm, then BF =? Cm
• 4. As shown in the figure, AE bisects ∠ BAC, BD = DC, de ⊥ BC, EM ⊥ AB, en ⊥ AC
• 5. As shown in the figure, AE bisects ∠ BAC, BD = DC, de ⊥ BC, EM ⊥ AB, en ⊥ AC
• 6. As shown in the figure, AE bisects ∠ BAC, BD = DC, de ⊥ BC, EM ⊥ AB, en ⊥ AC
• 7. As shown in the figure, AE bisects ∠ BAC, BD = DC, de ⊥ BC, EM ⊥ AB, en ⊥ AC
• 8. In the RT triangle ABC, the angle B = 90 ° ED is the vertical bisector of AC, intersecting BC and AC at points E and D respectively, connecting AE, if the angle BAE: the angle BAC = 1:5
• 9. It is known that in △ ABC, D is the midpoint of AB, e is the point on AC, EF ‖ AB, DF ‖ be. (1) conjecture: the relationship between DF and AE is______ Try to explain the correctness of your conjecture
• 10. In the triangle ABC, point O is a moving point on the side of AC. when passing through point O, a straight line Mn is parallel to BC. Let the bisector of the intersection angle BCA of Mn be at e, and the bisector of the intersection angle BCA be at E Bisector at point F. (1) proof; EO = fo, (2) when point O moves to where, quadrilateral aecf is rectangular, prove your conclusion
• 11. As shown in the figure, ABC = ADC = 90 °, M is the midpoint of AC, Mn ⊥ BD and N, and BN = nd is proved ditto
• 12. As shown in the figure, it is known that in △ ABC, the bisector of ∠ ABC intersects with the vertical bisector of AC side at point n, passing through point n makes nd ⊥ AB at D, NE ⊥ BC at e, and proves ad = C Verification: ad = CE
• 13. Known: as shown in the figure, BD is the angular bisector of △ ABC, EF is the vertical bisector of BD, and intersects AB at e and BC at point F
• 14. Known: as shown in the figure, BD is the angular bisector of △ ABC, EF is the vertical bisector of BD, and intersects AB at e and BC at point F
• 15. In the right triangle, ∠ ACB = 90 °, CD is high, e is the middle point of BC, the extended line of ED and the extended line of Ca intersect at point F, and AC: BC = DF: CF is calculated
• 16. In △ ABC, ACB is 90 ° and CD ⊥ AB is made at d through point C. e is the midpoint of BC. Connect ed and extend the extension line of intersection CA to F. verify: AC / DF = BC / CF In △ ABC, ∠ ACB = 90 °, make CD ⊥ AB at d through point C, e is the midpoint of BC, connect ed and extend the extension line of intersection Ca at F. verification: AC / DF = BC / CF
• 17. In the triangle ABC, the vertical bisectors of edges AB and AC intersect point P. it is proved that point P is on the vertical bisector of BC It's an equilateral triangle
• 18. It is known that the abscissa of point a (- 2,0), B (4,0) P on the image of function y = 1 / 2x + 2 is m. when the triangle PAB is a right triangle, the value of M is obtained When p is a right angle
• 19. For example, the image of the first-order function y = - 2 / 3x + 2 intersects with the x-axis and y-axis at point AB respectively. With the line AB as the edge, the isosceles triangle ABC is made in the first quadrant, ∠ BAC = 90 ° For example, if there is a point P on the intersection D of AC and y-axis, OA, and the intersection ab of the vertical line of x-axis, AC is at two points m and N, if Mn = 1 / 3bd, the P coordinate is?
• 20. The first-order function y = 3 / 2x + 3 and y = - 1 / 2x + Q both pass through a (m, 0) and intersect with y axis at points B and C 1 respectively. Try to find the area of △ ABC. 2. Point D is a plane The linear functions y = 3 / 2x + 3 and y = - 1 / 2x + Q pass through a (m, 0) and intersect with y axis at points B and C respectively 1. Try to find the area of △ ABC 2. Point D is a point in the plane rectangular coordinate system, and the quadrilateral with points a, B, C and D as the vertex is a parallelogram. Please write the coordinates of point d directly 3. Can we draw a straight line through the vertex of △ ABC, so that it can divide the area of △ ABC equally? If we can, we can find the functional relationship of the straight line; if not, we can explain the reason