The moving point on the side of BC (not coincident with B and C). The vertical line passing through e is straight line AB, and the vertical foot is F.
The extension lines of FE and DC intersect at G point, connecting DE and DF. ....
( 1)
Verification: BEF
√δCEG。
(2)
What is the relationship between the perimeter of △BEF and △CEG when point E moves on BC line? And explain your reasons.
(3) let be = x, and the area of △DEF is
Please find out the functional relationship between y and x, what is the value of x, and what is the maximum value of y?
(Analysis of 27 Questions in Chenzhou, Hunan Province in 2008) (1)
Because the quadrilateral ABCD is a parallelogram,
therefore
1 point
therefore
therefore
3 points
(2)
The sum of the perimeters of is a constant value.
4 points
Reason 1: When FG crosses the parallel line of point C and intersects the straight line AB in H ..
Because GF⊥AB, quadrilateral FHCG is a rectangle. therefore
FH=CG,FG=CH
Therefore,
The sum of the perimeters of is equal to BC+CH+BH.
pass by
Bc = 10, AB = 5, AM = 4, CH = 8, BH = 6,
So BC+CH+BH = 24.
. . . 6 points
Reason 2: As can be seen from AB = 5 and AM = 4,
In Rt△BEF and Rt△GCE, there are:
So the circumference of △BEF is
△△ ECG circumference is
And be+ce = 10, so
The sum of perimeters is 24.
6 points
(3) let be = x, then
therefore
8 points
Formula:
.
So, when?
When y has the maximum value.
9 points
The maximum value is
.
10 point
Example 3. (08 Wenzhou, Zhejiang) As shown in the figure, in
Yes,
They are the edges.
The midpoint of.
From the point of view,
Leave the edge
Direction movement, crossing point
work
what
, a little.
work
transmit
what
, when the key.
Yudian
When overlapping, the points
Do n't move a set of
.
(1) Find the point
reach
distance
Length;
(2) seeking
About; In all parts of; about
Function relation of (no need to write the range of independent variables);
(3) Is it meaningful?
, make
Isosceles triangle? If it exists, request all those that meet the requirements.
The value of; If it does not exist, please explain why.
6.
Solution: (1)
.
main points
for
Midpoint,
.
.
.
(2)
.
, namely
About; In all parts of; about
The functional relationship of is:
.
(3) Existence can be divided into three situations:
① When?
When, a little.
work
what
, then
.
.
.
② When?
When,
.
③ When?
So, when?
for
A point on the vertical, so it is a point.
for
The midpoint of,
.
All in all, when
for
Or 6 or
When,
It is an isosceles triangle.
46. (Qingdao, Shandong, 2009) As shown in the figure, in the trapezoidal ABCD,
, point
Starting from B, move at a constant speed along the BD direction at the speed of 1 cm/s; At the same time, the line segment EF starts from DC and moves in the direction of DA at a constant speed of1cm/s.
At q, connect PE. If the exercise time is
(s)(
). Answer the following questions:
(1) When
Why are you on duty?
?
(2) Settings
The area of is
(cm2), find
and
The functional relationship between them;
(3) Is there a moment?
, make
? If it exists, find out this time.
The value of; If it does not exist, explain why.
(4) Connection
In the above movement, the Pentagon
Has the area changed? Explain why.
Congruent triangles's nature and judgment, similar triangles's judgment and calculation.
Answer: (1)√.
∴
. and
,∴
,∴
.
Suffer from hell
.
(2)∵
Parallel and equal
Quadrilateral
It is a parallelogram.
.
∵
,∴
. ∴
. ∴
.
. ∴
.
Guo b Zuo
, pay
what
, too
work
, pay
what
.
.
∵
,∴
. and
.
(3)
. if
, yes
solve
.
(4) in
and
Yes,
∴
.
∴ In the process of movement, pentagons
The area of the remains unchanged.
High school final exam summary reflection 600 words 1
Although I took this exam in the first w