1. What kind of triangle is called an isosceles triangle?
2. Point out the waist, bottom edge, top angle and bottom angle of isosceles triangle, which is the first teaching plan of junior high school mathematics.
(First, the teacher asks questions to understand the mastery of the preparatory knowledge, and the students think and answer orally. )
(2) Construct suspense and create situations:
3. What are the characteristics of a general triangle? (Three sides, three internal angles, height, center line, angle bisector)
4. Besides the characteristics of general triangles, what are the special features of isosceles triangles?
Take question 3 as the starting point of teaching to stimulate students' interest in learning. The fourth question left the students in suspense. )
(3), goal-oriented, natural introduction:
In this lesson, let's learn 9.3 isosceles triangle together.
(blackboard writing topic) 9.3 isosceles triangle (understand the content of this lesson)
(4) ask questions and try to explore:
Combined with question 4, please take out isosceles triangles with different specifications and demonstrate (model) the experiment that isosceles triangles are axisymmetric figures with the teacher to guide students to observe the experimental phenomenon.
[Question] What conclusion did you find through observation?
(Let the students point out their findings through experiments or demonstrations, guide them, and summarize them one by one with standardized mathematical language, and finally get the characteristics of isosceles triangle. )
【 Conclusion 】 The two base angles of isosceles triangle are equal.
(The conclusion that the students found on the blackboard)
Characteristics of isosceles triangle 1: the two base angles of isosceles triangle are equal.
In △ ABC, AB = AC ()
∴∠B=∠C()
[Methods] Students can think in a variety of ways, and associate the knowledge and methods they have learned vertically and horizontally, laying the foundation for the proof of the proposition.
Example 1: It is known that in △ABC, AB = AC, ∠ B = 80, and the number of times to find ∠C and ∠ A.
[Students think, teachers analyze, write on the blackboard]
Practice thinking: textbook P84 Exercise 2 (The base angle of an isosceles triangle can be a right angle or an obtuse angle? Why? )
[Continue to observe the pattern of the experimental paper] (The following contents may have been put forward by students in previous experiments)
[Question] What line may be the' symmetry axis' of the isosceles triangle in the text?
Cultivate students' ability to sum up math problems by asking questions, questioning, group discussion and summing up.
[Guide students to observe] The crease AD is the symmetry axis of the isosceles triangle. What line might the advertisement be?
Students found that AD is the bisector of the top angle, the midline of the bottom and the height of the bottom of an isosceles triangle.
【 Conclusion 】 The bisector of the top angle, the height on the bottom edge and the midline on the bottom edge of an isosceles triangle coincide, which is called "three lines in one" for short.
Isosceles triangle feature 2:
The bisector of the top angle, the middle line and the high line of the bottom of the isosceles triangle coincide (three lines are one)
(showing the small blackboard)
[Fill in the blank] Inferred from the characteristics of isosceles triangle, in △ABC
( 1)∵AB=AC,AD⊥BC，
∴∠_=∠_,_=_;
(2)∵AB=AC, and AD is the midline.
∴∠_=∠_,_⊥_;
(3)∵AB=AC, AD is the angular bisector,
∴_⊥_,_=_
Through intuitive mold demonstration, draw inference 2, show the application method of small blackboard [fill in the blank] and "three lines in one", junior high school mathematics teaching plan "isosceles triangle-junior high school mathematics teaching plan volume I" Fill in the blanks to impress students and understand the application method of three-in-one
Emphasizing the importance of the pre-attribute of the three-line segment in the "three-line integration" feature can enable students to draw and verify.
(5), inspiration and induction, preliminary application:
Example 2: As shown in the figure, in △ABC, AB=AC, D is the midpoint on the side of BC,
∠ b = 30, find∠1and∠ ∠ADC degrees.
Classroom exercises:
(1)P85 Exercise 3
(2) Known example 3: As shown in the figure, the top corner of the building is ∠BAC = 100, the column passing through the roof A is AD⊥BC, and the roof rafter AB = AC. Find ∠ B, ∠C, ∠BAD, ∠ on the top shelf.
This is a geometric calculation problem. Students should deepen the application of the content of this lesson and guide them to write out the problem-solving process.
(6), summarize and strengthen the thought:
(1) Describe the characteristics of isosceles triangle and its application;
(2) Using the characteristics of isosceles triangle, it can be proved that two angles are equal, two line segments are equal and two straight lines are perpendicular to each other.
(3) Association method should be used frequently, which is of great benefit to solving problems in the future.
(7), homework guidance preview:
P86 Exercise 9.3 1, 3,4 Preview textbook: P85 isosceles triangle
Thinking after class: Are the midlines (high lines) on the two waists of an isosceles triangle equal? Why?