The contents in brackets "[]" are explanatory. I'll give them to you. Don't copy them as answers!
1、? [There is something wrong with the topic! I've been thinking about the first question for a long time and I can't figure it out! The title is wrong! The condition is "angle B= angle D=90 degrees" instead of "angle B= angle C=90 degrees"! ! ! ]
Now that you have made it, I won't say much!
2、? [The second question, when you say you want to prove it, is to prove it as a proof problem. I think this question should be written as a solution, and it will be more appropriate to use the steps of the solution! ]
(2)? [This is entitled auxiliary line. If we first "extend AD to E to make DE=BA", it will be difficult to do so. It will be much easier to "do CE‖BA at point C and hand in the extension line of AD at point E"! ]
Solution:? [Draw a picture first, and the picture should be completed according to the part I answered! ]
Point C is CE‖BA, and point E is the extension line of AD.
∫∠DAB = 120
∴∠DEC=60
∫AC is the bisector of∝∠ ∝∠DAB.
∴∠DAC=∠BAC=∠DAC=60
△ ace is an equilateral triangle.
∴EC=AC？ [Use the "Angular Edge (AAS)" relationship to prove △ EDC △ ABC, and find the edge relationship! ]
∠∠ADC and ∠ABC are complementary, ∠ ADC+∠ EDC = 180.
∴∠EDC=∠ABC？ 【 Prove △ EDC △ ABC with "Angular Edge (AAS)" relation and find the first angular relation! ]
∠∠DEC = 60 =∠BAC？ 【 Prove △ EDC △ ABC with "angle edge (AAS)" relation, and find the second angle relation! ]
∴△EDC≌△ABC
∴ED=AB
AE = AC
∴AB+AD=ED+AD=AE=AC
∴ The quantitative relationship among AB, AD and AC of line segment is AB+AD=AC.
Among them, I use the geometric auxiliary line method, and this tired problem can also be done by vector method, because the proof method of vector method is relatively simple. Ask the teacher and you will know the steps. They are almost the same and there is no challenge, so I won't say much here! ]
3、? This question is an in-depth study of the previous question. The main investigation is to do parallel auxiliary lines to complete the graphics! The steps to solve the problem are similar to the second question. Since you only want answers, I'll just give them. ]
AB+AD= (the root of two) AC? 【 "the root of two" can't be typed! I sent a picture! ]
[This kind of topic can be further deepened! If the angle of condition ∠DAB is changed to ∠DAB=α! Then the answer is "AB+AD=(cos(α/2))AC"! You use this expanded content to test the teacher, and the teacher must think for a while! ]
【 Hee hee! It's done. ]