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Isosceles triangle and analysis of the nature of the case


papers Posted: 2011-04-22 Paper Source: www.teachpaper.com papers published by: Teaching Teaching Papers Papers Hits: second isosceles triangle and analysis of the nature of the case: to enable students to ask questions in the experiment, problem-solving approach, and unwittingly into the learning environment, the students from passive learning into active learning habits like . : The nature of the isosceles triangle is the eighth-grade mathematics content, it is in the understanding of the axial symmetry and understand the basis of congruent isosceles triangles to determine the nature of the case and analysis
: isosceles triangle is the nature of eighth-grade math of the content, it is to know and understand the symmetry axis to determine congruent triangles on the basis of. The key learning isosceles triangle proved equal to the next corner, and two straight line segments perpendicular to each other equal basis, so this lesson has important nexus role.
: other side of the isometric nature of the three-in-one thinking to solve problems
1, three lines-one of this nature provided that the triangle is isosceles, if known on the center line, the bottom edge of the high The triangle is an isosceles triangle, isosceles triangle on the grounds that 2, the edge in the solution of an isosceles triangle, angle calculation problems, the conditions are not clear-cut case, according to subject characteristics, the nature of the isosceles triangle, triangle and trilateral relations of angles and triangles theorem analysis and discussion, otherwise easily cause leakage of the solution or wrong solution.

one, Teaching target
1, to enable students to master the nature of the isosceles triangle theorem and corollary.
2, so that students master the theory of isosceles triangle theorem and the nature of the method of proof,Oakley sunglasses sale, and can use nature of the problem-solving.
3, students explore the development of knowledge.
Second, the teaching emphasis and difficulty
1, focus: the nature of the isosceles triangle and the discovery of inference and reasoning processes; nature of the theorem and the use of inference.
2, and difficult: the use of Corollary 1.
3, doubt: isosceles triangle,tory burch outlet,
set to pay attention to distinguish between questions and conclusions, application language to be accurate, as not to
Third, the teaching methods

four guided discovery method of teaching methods
collapsible cardboard isosceles triangle, projector or multimedia teaching aids.
Fifth, the teaching process
review questions
1, What is an isosceles triangle? It is all part of the name? .
2, isosceles triangle with the general nature of it? It's a relationship between three sides, angles, and how much?
introduction of new courses. As the isosceles triangle has two equal sides, angles, and also 180 °, then the students think of an isosceles triangle with the angle between the angle, and the angle between the side there is no other relationship? That is we have to study.
blackboard issue: the nature of the isosceles triangle
Demo: ready to fold the cardboard isosceles triangle as shown in Figure 3-68 first two stacked waist, students observed that the overlap each other,
explain the lesson
1, the nature of the isosceles triangle theorem: two at the end
angle isosceles triangle are equal.
known: Figure 3-68, △ ABC in,replica oakley sunglasses, AB = AC
Prove: ∠ B = ∠ C
Note: isosceles triangle specification wording: △ ABC in, AB = AC to show both sides of this isosceles
continue to guide the students to observe: to inspire students to see the commencement of cardboard, folded back into a isometric AD and two, that is the angle bisector of the crease, and crease on both sides is congruent shape, it can discover the method of proof of the theorem.
Students can explore three different methods of adding auxiliary lines of evidence:
Method 1: the bisector of ∠ A for AD, is congruent with the SAS card.
Method 2: for AD ⊥ BC in D, is congruent with the HL license.
Method 3: for the BC side of the center line AD, is congruent with the SSS Card.
allow students to choose an approach to prove theorems, the teacher can use the projection method in three different cards displayed. We can see from the above process: BD = DC, ∠ ADB = ∠ ADC = 90 °, AD split BC, it was deduced 1.
2, Corollary 1: isosceles triangle angle bisector and perpendicular to the bottom hemline split.
namely: isosceles triangle angle bisector, bottom middle, bottom edge of the high line
overlap each other,
Figure 3-69: △ ABC side of an equilateral triangle, AB = BC = CA,
from the other side of the isometric know: ∠ A = ∠ B = ∠ C, by the triangle
angles and the theorem is Corollary 2
Corollary 2: equilateral triangle all angles are equal, and each interior angle of 60 °
Enlightenment: The nature of the isosceles triangle has an important role in the use of the nature of Theorem may permit the same corners, the use of Corollary 1 can permit two segments are equal, two angles are equal and the two lines perpendicular to each other. Corollary 2 can be proved with an angle of 60 ° or by making an equilateral triangle to make a 60 ° angle.
3, isosceles triangle in nature known application
Example 1: Figure 3-70, the housing angle ∠ ABC = 100 °
A roof over the column AD ⊥ BC, rafters AB = AC,
find: the top shelf ∠ B, ∠ C,mbt cipő, ∠ BAD, ∠ CAD degree.
This is a geometry problem, guide students through the process of problem solving analysis
specification, so that students understand the math familiar with the steps, their ability to apply knowledge to solve practical problems.
supplementary exercises:
a known angle of isosceles triangle 130 °, find the other corners of the degree.
a known angle of isosceles triangle 70 °, find the other corners of the degree.
isosceles triangle in the relationship between angle and corner.
△ ABC in the AB = AC, then ∠ A = 180 ° -2 ∠ B = 180 ° -2 ∠ C
known degrees of an angle isosceles triangle, find the other corners, if angle is obtuse or right angle are known,ed hardy uk, then it must be angle, acute angle if the angle is known, it may also be angle corner.
isosceles triangle theorem and the corollary of the nature of content and applications.
practice. Materials P. 67 1,2,3
operations. Materials P. 72 in, 2,3,4,5
blackboard design
1, viewing life in the picture into the subject
2, paper-cutting activity leads to the concept of isosceles triangle
paper cutting required observed characteristics of the triangle-shaped isosceles triangle concept
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