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

Because the intersection point of the vertical bisectors of the edges AB and BC is p, that is pa = Pb, PA = PC, Pb = PC. according to the property of the angular vertical bisector (the distance from each point of the vertical bisector to both ends of the line segment is equal), that is, the point P is on the vertical bisector of BC

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1. 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
2. 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
3. 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
4. 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
5. 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
6. As shown in the figure, ABC = ADC = 90 °, M is the midpoint of AC, Mn ⊥ BD and N, and BN = nd is proved ditto
7. 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,
8. 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
9. 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______ ．
10. 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
11. 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
12. 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?
13. 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
14. If we know that the images of the linear functions y = 3 / 2x + m and y = 1 / 2x + n pass through point a (2,0) and intersect with y axis at two points B and C respectively, then the area of △ ABC is
15. If we know that the image of a linear function y = 2x + A, y = - x + B passes through a (- 2,0) and intersects with y axis at two points B and C respectively, then the area of △ ABC is () A. 4B. 5C. 6D. 7
16. The first-order function y = x + 3 and X, Y axis intersect at two points a and B respectively, and there is a point P on the coordinate axis, so that the triangle ABP is a right triangle, and the coordinates of point P are obtained
17. As shown in the figure, it is known that there are two points a (- 2,0), B (4,0) in the plane rectangular coordinate system, the point P in the first-order function y = 2 / 1 x + 2 / 5, and △ ABP is a right triangle Find the coordinates of point P
18. We know that the first-order function y = - 2x + 4 intersects with the x-axis and y-axis, and points a and B (1) make the isosceles triangle ABP with ab as the edge, if P is in the first quadrant (1) Make an isosceles triangle ABP with ab as the edge. If P is in the first quadrant, ask for the coordinates of point P (2) Under the conclusion of 1, make a parallel line of line AB through point P, intersect the x-axis, Y-axis with point C and point d respectively, and calculate the area of quadrilateral ABCD The first question is wrong. It's an isosceles right triangle
19. In the triangle ABC, a square tanb = b square Tana, judge the shape of the triangle
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