Symmetrical with the straight line EF.
(1) Draw a straight line ef;
(2) The straight line MN and EF intersect at point O, and try to explore the quantitative relationship between ∠ Bob "and the acute angle α of the straight line MN and EF.
Test center:
Drawing-axisymmetric transformation.
Special topic:
Drawing questions; Query type.
Analysis:
(1) perpendicular bisector who finds and connects key points and connects them; (2) According to the symmetry, find out the equal angle, and then make reasoning.
Answer:
Solution: (1) Connect B' b "as shown in the figure. (1 min)
Perpendicular bisector. (2 is the line segment b' b "(2 points).
Then the straight line EF is the symmetry axis of △ a ′ b ′ c ′ and △A″B″C″. (3 points)
(2) connect b 'o.
∵△ABC and△ a' b' c' are symmetric about the straight line MN,
∴∠ BOM = ∠ B 'om。 (5 points)
∫△A'b'c' and △ a "b" c "are symmetrical about the straight line EF,
∴∠ Bue = ∠ Bue. (6 points)
∴∠bob″=∠bom+∠b′om+∠b′oe+∠b″oe=2(∠b′om+∠b′oe)=2α
That is, ∠ Bob "= 2α. (7 points)
Comments:
To solve this problem, we should understand the essence of axial symmetry:
1. The symmetry axis is a straight line.
2. A straight line perpendicular to and bisecting a line segment is called the perpendicular bisector of the line segment, or the vertical midline. The distance between the point on the vertical line in the line segment and both ends of the line segment is equal.
3. In an axisymmetric figure, the distance between the corresponding points on both sides of the axis of symmetry is equal.
4. In an axisymmetric figure, the axis of symmetry divides the figure into two equal parts.
5. If two graphs are symmetrical about a straight line, then the symmetry axis is the middle perpendicular of the line segment connected by any pair of corresponding points.