∫AB∨CD
……
①∴∠DHA=∠FDE
∠haf =∠def \f is AE midpoint ∴AF=FE∴△DEF.
≌△HFA∴DE=AH
H is the midpoint of AB ∴HB=DE.
……
② According to ① ②, the quadrilateral DEBH is a parallelogram ∵DH∨eg, and E is the midpoint of DC ∴EG is the midline of △CDF ∴GF=GC 2. It is a synthesis problem of rectangular inverse proportional function, as shown in the figure, in rectangular ABCD, AB=5.
AD=2, point P is the moving point of BC, DE⊥AP and foot E, if AP=X, DE = Y. Try to find the functional relationship between Y and X, and determine the value range of user-defined X. Solution:
In △ABP and △DEA
∠∠ABP =∠DEA = 90
∠DAE=∠BPA
(Two straight lines are parallel and the internal dislocation angles are equal)
∴△ABP∽△DEA
∴AB/AP=DE/DA
5/x=y/2
That is, the functional relationship is y =10/x.
∵
5 & ltAP & lt√29
(under 29 signs)
functional domain
5 & ltx & lt√29
3. As shown in the figure, O is the center of square ABCD, BE bisects ∠DBC, passes through DC at point E, extends BC to point F, makes CF=CE, connects DF, and passes through the extension line of BE at point G, connects OG. What if DG? = 4-2 √ 2 (√ 2 = root number 2), find the area solution of square ABCD: ∵BC=DC, ∠BCD= angle dcf = 90, CE = CF ∴△ BCE △ DCF ∠ F =
(
Divided ∠DBC)∴△BDG≌BGF∵DG?
=4—2√2=(2—√2)? ∴ gf = DG = 2-√ 2df = DG+gf = 2 (2-√ 2) Let the side length of a square be xbd = BF = √ 2xcf = BF-BC = √ 2x.
—x=(√2— 1)x DC in Rt△DCF？ +CF？ =DF？ x？ +(√2— 1)? x？ =4(2—√2)? x？ (4—2√2)=4(4—2√2)x？ =4 square ABCD area is x? =4
4. As shown in the figure, in Rt△ABC, ∠ A = 90, AB = AC = the square root of 8.
Point E is the midpoint of AC, and point F is on the bottom BC. What is the area of FE⊥BE? Solution:
As shown in the figure, e is used as EH⊥BC in H.
Let EH=
x
∫∠A = 90，AB=AC
∴
△CEH is also an isosceles right triangle.
HC=EH=
x
∵
E is the midpoint of AC.
∴
AE=AC=4√6
∴
x^2+x^2=(4√6)
∴
2x^2=96
∴x=4√3
BC=√(AD^2+AC^2)= 16√3
BH = 16ì3-4ì3 = 12ì3
Yi Zheng △EHF∽△BHE
HF/EH=EH/BH
HF=48/( 12√3)=4√3/3
FC=4√3-4√3/3=8√
S△CEF=FC×x
/2
=8√3/3×4√3/2
= 16
Hello!
Sorry, the teacher answered you two days late. These questions are more difficult, and I chose them from answering other people's questions for your study! If you have any questions, please ask. I hope it helps you.
^_^