As shown in the figure, it is known that in the triangle ABC, ab = AC, ad is the height on the edge of BC, and point P is in the triangle abd

Prove: because ABC is isosceles triangle, so D is the midpoint of BC, because P is in abd, so angle BAP is less than angle cap, in triangle BCP, because BP is less than PC, so angle PCB is less than angle PBC, so angle ACP is greater than angle ABP, so angle APB > angle APC

RELATED INFORMATIONS

1. As shown in the figure, it is known that triangle ABC is an equilateral triangle, point P is any point on BC, and triangle AQP is also an equilateral triangle. Prove that triangle AQB ≌ triangle APC
2. As shown in the figure, BD is the height on the side of equilateral △ ABC, extend BC to e, so that CE = CD, (1) try to compare the size relationship between BD and De, and explain the reason; (2) if BD is changed to the angular bisector or median line of △ ABC, can we draw the same conclusion?
3. Mathematics problems in grade two of junior high school (equilateral triangle) In △ ABC, ab = AC, ∠ BAC = 120 °, the vertical bisector of AB intersects BC at E. prove: be = half CE
4. As shown in the figure, given that points B, C and D are on the same straight line, △ ABC and △ CDE are equilateral triangles. Be intersects AC at F, ad intersects CE at h. ① verify: △ BCE ≌ △ ACD; ② verify: CF = ch; ③ judge the shape of △ CFH and explain the reason
5. In the eighth grade mathematics equilateral triangle ABC, there is a point P, AP is equal to 3, BP is equal to 1, CP is equal to 5?
6. EA is the tangent line of circle O, a is the tangent point, the chord BC intersects OA at D, through B makes Pb, vertical CB intersects EA extension line at P
7. As shown in the figure, AB is the diameter of ⊙ o, Pb is tangent to ⊙ o at point B, the extension line of chord AC ∥ OP and PC intersects BA at point D, proving that PD is tangent to ⊙ o
8. AB is the diameter of the circle O, Pb tangents the circle O to B, D on the circle O, ad ‖ Po, prove that PD is the tangent of the circle o
9. It is known that: as shown in the figure, △ ABC is the inscribed triangle of O, the bisector of angle ACB intersects circle O at point D, and makes tangent l of circle O through point D. prove that AB is parallel to L
10. It is known that: as shown in the figure, △ ABC is the inscribed triangle of ⊙ o, ⊙ O's diameter BD intersects AC at e, AF ⊥ BD at F, extending AF intersects BC at g. the proof is AB2 = BG · BC
11. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
12. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
13. P is a point in the equilateral triangle ABC, PC = 5, PA = 3, Pb = 4, find the degree of angle APB There are only four points a, P, B, C
14. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
15. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
16. Given the triangle ACP, similar to the triangle ABC, AC = 4, AP = 2, find the length of AB? (PC connected) a P B C
17. As shown in the figure, we know that in △ ABC, P is the point on AB, connecting CP, when the condition is satisfied______ When △ ACP ∽ ABC
18. As shown in the figure, it is known that △ ABC, P is a point on edge ab. when connecting CP, (1) ACP satisfies what conditions, △ ACP is similar to △ ABC? (2) AC: AP is full
19. As shown in the figure, it is known that △ ABC, P is the point on AB, connecting CP. in the following conditions, △ ACP ∽ ABC cannot be determined as () A. ∠ACP=∠BB. ∠APC=∠ACBC. ACAP＝ABACD. ACAB＝CPBC
20. As shown in the figure, in RT △ ABC, ∠ ACB = 90 ° AB = 6, P is the point on AB, connect PC, set ∠ BCP = m ∠ ACP, when AP = 3 / 2, whether there is a positive integer m, Make PC perpendicular to ab? If it exists, calculate the value of M. if it does not exist, explain the reason