Conducting a geometry lesson on the topic "Signs of equality of right-angled triangles"
Posted: Jun 06, 2021
Lesson objectives.Educational: systematization of knowledge, abilities and skills on the use of signs of equality of right-angled triangles in solving problems, including those with practical content.Developing: development of interest in the subject, attention, logical thinking, mathematically literate speech; information and communication competencies of students.Educational: education of the communicative qualities of a person; independence, responsibility, perseverance, aesthetic taste.
Lesson Objectives:1) In the direction of personal development: to instill in students an interest in geometry and knowledge. Form a positive motive for learning. To contribute to the formation of the communicative competence of students, the ability to organize educational cooperation and joint activities with the teacher and peers, to be objective in assessing the activities of both their own and others. Develop observation, the ability to compare, analyze and draw conclusions, the ability to pose a problem and look for ways to resolve it. To form a responsible attitude towards educational work.
- In the metasubject direction: to form students' ideas about a geometric figure - a triangle, as an integral part of the world around us, on the different use of objects and devices in the form of a triangle in everyday life and life. Show students how to describe a practical life task in mathematical language, the ability to search and further apply knowledge gained in other subject areas in mathematics lessons.
- In the subject direction:
Know: formulations of signs of equality of right-angled triangles.
Be able to: solve problems, including those with practical content, using the signs of equality of right-angled triangles.
Analyze: the possibility of using a particular feature in solving various problems.
I. Organizational stage
Purpose: the inclusion of students in activities at a personally meaningful level. "I want it because I can."
Student activity: inclusion in a business rhythm, a positive emotional orientation should arise.
Teacher activity: oral communication. Students' interest in the lesson is generated by communicating why geometry places a lot of emphasis on right-angled triangles.
To have enough energy for the entire lesson, let's do a physical minute.
We have a geometry lesson with you today. I think all of you have noticed the inscription "He who has not studied geometry, let him not enter this door", which the Greek scientist Plato ordered to do over the door of his house. It is no coincidence that Greek scientists did so much mathematics. It is not by chance that Plato's inscription speaks of geometry, and not of mathematics in general. The Greeks considered geometry to be a particularly important science.
You may be wondering: Why does geometry pay special attention to a right-angled triangle, although objects of this shape are not often found?
As in chemistry, first the elements are studied, and then their compounds, in biology - unicellular, and then multicellular organisms, so in geometry - points, segments and triangles, of which other geometric shapes are composed.
Among these figures, a right-angled triangle plays a special role. Indeed, any polygon can be divided into triangles, knowing how to find the angular and linear elements of these triangles, you can find all the elements of the polygon. In turn, any triangle can be divided by one of its heights into two right-angled triangles, the elements of which are connected by a simpler relationship. You can find the elements of the triangle. If we reduce the problem to solving these two right-angled triangles.
II. Updating basic knowledge
Purpose: repetition of the studied material, updating the basic knowledge necessary for further work in the lesson.
Let's remember what topic we studied in the last lessons? (Signs of equality of right-angled triangles)
Today we will continue to work on solving problems using the signs of equality of right-angled triangles. Write down the number, cool work. Topic "Signs of equality of right-angled triangles". You have on your desks the flow charts of the lesson, where you will evaluate yourself at each stage of the lesson.
Now, in pairs, you will check each other for knowledge of the wording of the signs of equality of right-angled triangles and put points in the flowchart of the lesson.
Mutual examination: students check each other's knowledge of the wording of signs of equality of right-angled triangles and put grades on a self-assessment sheet.
Updating basic knowledge.
The sum of two acute angles of a right-angled triangle is... 90 °.The leg of a right-angled triangle lying opposite an angle of 30 ° is equal to... half of the hypotenuse.Find the sharp corners of a right triangle if one is 50% larger than the other. (decision)
In a right-angled triangle, the median drawn from the vertex of the right angle is... half the hypotenuse.The outer angle of a triangle is equal to the sum... of the two angles of the triangle that are not adjacent to it.
Solution of word problems.
1. One of the corners of a right-angled triangle is 60 °, and the sum of the hypotenuse and the smaller leg is 18 cm. Find the hypotenuse and the smaller leg.
Given:?ABS, C = 90 °, A = 60 °, AB + AC = 18cmFind: AB, AC.Decision:B = 90 ° - 60 ° = 30 °, which means that AC is a smaller leg, thenAC = 0.5ABAB + 0.5AB = 18AB = 12cm, AC = 6cmAnswer: AB = 12cm, AC = 6cm.
2. In a right-angled triangle ABC C = 90 ° and A = 30 °, the median CM and the bisector MD???? are drawn. Find MD if BC = 23cm.
Given:????,? = 90 °,? = 30 °,??-median?,?D - bisector????,?? = 23cm.Find: MD.Decision:Because CM is the median, then CM-BM = MA = 0.5ABBecause A = 30 ° and BC = 24cm, then AB = 46cm and = CM = BM = MA = 23cm.Because CM = MA, then?CMA is isosceles, therefore, MD is height.Because A = 30 °, ADM = 90 ° and MA = 23cm, then MD = 0.5MA = 11.5cm.Answer: MD = 11.5cm.
Pedagogical activity is a purposeful, motivated influence of the teacher, focused on the all-round development of the child's personality and preparing him for life in modern socio-cultural conditions.