In the operation, the right vertex E of the triangle DEF is placed on the hypotenuse AC of the triangle ABC, and then the triangle DEF is rotated around the point E, so that the edge DE and the edge AB intersect at the point P, and the edge EF and the edge BC are at the point Q..
To explore a way to make a difference,
(1) As shown in Figure 2, when CE/EA= 1, what is the quantitative relationship between EP and EQ? And give proof.
(2) As shown in Figure 3, when CE/EA=2, what is the quantitative relationship between EP and EQ? , and explain the reasons.
(3) According to your query results of (1) and (2), try to write the quantitative relationship between EP and EQ when CE/EA = m..
Is _ _ _ _ _ _ _, where the value range of m is _ _ _ _ (write the conclusion directly without proof).
Explore two ifs, AC = 30cm, continuous PQ, and let the area of △EPQ be S(cm2). During the rotation:
Is there a maximum or minimum value for (1) S? If it exists, find the maximum or minimum value, if it does not exist, explain the reason.
(2) With the different S values, what happened to the corresponding △EPQ number? The value range of the corresponding s value cannot be found.
∫AB/DE = BC/EF = AC/DF = 3/ 1
∴△ABC∽△DEF，
The similarity rate is 3/ 1.
The height ratio on the corresponding sides AB and DE is also equal to the similarity ratio, that is, 3/ 1.
∫ The height of the AB side is 24.
The height of ∴DE is: 24× 1/3=8.
thank you