Solving triangles Methodical development on geometry (grade 9) on the topic. Test Solution of rectangular triangles Test on the topic Solution of triangles

Purpose: Secure the knowledge of students with the sinus and cosine theorems, teach these theorems during solving problems.

Equipment:

tables with the image of triangles;
cards with formulas;
calculators;
brady's tables;
test for each student.

DURING THE CLASSES

I. Class organization. Check availability to the lesson. Message themes and objectives of the lesson.

II. Repetition of the material studied (or stage of workout)

1. Continue:

The square side of the triangle is equal to ... (cosine theorem)

2. Fill in the pass:

3. Continue:

The sides of the triangle are proportional to ... (sinus theorem)

4. Fill in the pass

5. Connect the line of part of the phrases corresponding to each other:

The solution of triangles is consisting

In finding unknown heights, median and bisector at the famous corners and sides of the triangle;

In finding an unknown perimeter at the famous corners and sides of the triangle;

In finding unknown parties and triangle angles according to its known corners and parties.

III. Fastening the material studied.

1. Solving tasks on finished formulas

Determine the formula that you need to find this unknown item:

cards with Formulas:

2. Solving tasks, pulling one of the cards:

IV. Intermediate control. Test for the whole class by options:

Option 1.

a) the square of any side of the triangle is equal to the sum of the squares of the other two of its sides;

b) the square of any side of the triangle is equal to the sum of the squares of the two other sides without a double product of these sides on the cosine of the angle between them;

c) the square of any side of the triangle is equal to the sum of the squares of the two other sides, minus the product of these sides on the cosine of the angle between them.

3. Cosine angle 120 ° is equal to ...

d) there is no correct answer.

4. Find sinus 29 ° 30 ". Emphasize the right answer:

5. To calculate the KMD in the triangle, you need to know ...

a) km, md, kd;

b) km, md ,;

d) there is no correct answer.

6. The sides of the triangle 5 cm and 4 cm, and the angle between them is equal to 30 °. Find the third side of the triangle.

Option 2.

1. Put the "+" sign next to the correct statement:

a) the side of the triangle is proportional to the sinus of opposite angles;

b) the sides of the triangle are inversely proportional to the sines of opposite angles;

c) The side of the triangle is proportional to the sines of opposite angles.

2. For this triangle, equality is true ...

3. Sinus angle of 135 ° is equal to ...

d) there is no correct answer.

4. Find cosine 67 ° 18 ". Emphasize the right answer:

5. In the triangle ABC are known the length of the side of the aircraft and the magnitude of the Corner S. To calculate AV, you need to know ...

d) there is no correct answer.

6. The sides of the triangle is 5 cm and 3 cm, and the angle between them is 60 °. Find a third side of the triangle.

Teacher KSU SOSH№ 30 - Kovalevskaya ON

In the lesson of geometry in the 9th grade, with the help of the presentation, various types of tasks on the topic of triangles are considered. When solving problems, special attention is paid to the correct selection of the theorem, which allows you to solve the problem most rational. To secure the studied material, it is proposed to perform a test test on the computer in Excel.

Thing:

Geometry 9 Class

Date:

03/02/2015

Occupation:

Subject:

Solving triangles

Common goals:

It is finishing and deepening students' knowledge about the theorems of sinuses and cosine and their use to solve triangles, as well as the ratio between the corners of the triangle and opposite parties.

Learning results:

improving interest in the subject

improving learning outcomes,

formation of skills of self and mutual education;

self and interconnection.

Key ideas:

Modules: "New approaches in teaching and learning", "Training of critical thinking", "Evaluation for training and evaluation of training", "Using ICT in teaching and training", "Training of talented and gifted students", "Teaching and training in accordance with Age features of students "," Management and Leadership in Learning ".

Geometry textbook for grade 9

Requisites:

Stickers, paper, markers, distribution material, Interactive board

During the classes:

Time

Stages lesson

Actions of the teacher

Actions of students

1 min

Org.Moment.

Greeting. Positive wishes for a lesson.

Responsiveness

1 min

Division into groups - 4 colors and 6 geometric figures (4 groups)

It makes it possible to choose each student from a geometric figure of a certain color. Explains the values \u200b\u200bof the figures:

Group Square- Leader

Parallelogram speaker

Rectangle - secretar

Outstanding, geniuses of ideas

Seed by groups in colors (blue, yellow, pink and red).

4 min

Brainstorming (orally)

The teacher asks questions:

Cosine theorem?

Sinus theorem?

Theorem on the sum of the corners of the triangle?

The formulas of bringing sharp and stupid angles for sinus and cosine?

Pupil Answers:

The square of any side of the triangle is equal to the sum of the squares of the two other sides without the double product of these sides on the cosine of the angle between them.

Triangle sides

proportional to sines of opposite angles.

The sum of the corners of the triangle is equal to 180̊ .

3 min

Brainstorming (written individual work)

According to the drawings, to record the sinus and cosine theores on the presentation and after performing checking the correctness of your record and evaluate yourself.

They write independently theorems on this drawing. At the end, the disciples are checked with the key of the teacher's answers on an interactive board and expose their points in the estimated sheets.

2 minutes

Brainstorming (orally)

The teacher asks questions. Type Types:

Solving triangles on the side and on two corners.

The solution of triangles on two sides and the corner between them.

The solution of triangles in three parties.

The solution of triangles on two strandes and the corner under contact with one of them.

Answer questions.

Pupil Answers:

Apply the theorem about the sum of the corners of the triangle and the cosine theorem.

Apply the theorem about the sum of the corners of the triangle and the theorem of the sinuses.

13 min

Mathematical dictation (written individual work)

According to the data drawings on the presentation slides, find an unknown element of the triangle, painting the theorems of sinuses and cosine. After performing checking on the board, the correctness of your record and evaluate yourself. Slides in the presentation are switched in time for the first 3 dadachi for 2 minutes, the last 2 to 3 minutes.

Pupils solve their own task. At the end, the disciples are checked with the key of the teacher's answers on an interactive board and expose their points in the estimated sheets.

1 min

Fizminutka for eyes

The teacher watches the students and sends to calm music

Positive setting

7 min

Pisa. : Solving a logical task on the poster (work in groups). Protection of the poster with the speaker comments from the group.

The teacher reads the task and proposes to solve it geometrically in the group. After asking for answers, all groups offers one of them to protect its solution.

The use of open and problematic issues to clarify how long students have understood the task. (56 trees)

Collection of information - the knowledge that they have at the time of the lesson (knowledge and understanding). While working, students can contact each other for help. Pupils in groups are trying to find a more complete explanation of the task.

10 min

Stage of consolidation and control of students' knowledge on this topic:

independent work in groups with dough

The teacher proposes to solve its own task, performing a test test on the computer in Excel.

1 min

Homework

Pupils are listening carefully and record homework.

3 min

Reflection stage. Summarizing.

The teacher asks to choose one of the 6 hats of thinking and try to give reflexion of the lesson and his knowledge at the end of the lesson. The basis of this method is the idea of \u200b\u200bparallel thinking. Parallel thinking - This is a constructive thinking, in which various points of view and approaches do not face, but coexist. Why hats? The hat is easy to wear and remove the hats indicate the role.

Evaluate their knowledge after the lesson. Control, correction, evaluation of a partner actions, skill with sufficient fullness and accuracy to express their thoughts.

« Surface"The hat has a definite flowers, students consider thinking in a given direction. Changing the hats teaches to see the same subject from different positions, resulting in shape the most complete picture.

Appendix No. 1:

Assessment Sheet (Group №1)

FI student

Assessments for tasks

Total assessment

Homework

Frontal survey

Mathematical dictation

Protecting poster

test

Additional assessment

Appendix number 2:

Test on the topic: "Decision of triangles".

I. Instructions for working with the test:

1. The tasks of the 1st test version are on the sheet 2. Setting the 2nd test version are located on a sheet 3. For switching - click LKM on the LED tab2 or sheet3.

2. After reading the next task, choose the correct answer. Then switch to the List1 tab and enter the number of the correct answer to the response table of your option.

3. Repeat item 2 instructions until you complete all tasks of the test.

4. The test is 10 minutes away. Check time on computer clock!

5. On the execution of the test report to the teacher. - Evaluation is logged.

II. Table response tables:

Option 1

Option 2

№ tasks

№ answer

№ tasks

№ answer

The number of correct answers:

Evaluation:

How to enter the number of the selected response:

1. Skylkni LKM (left mouse button) in the desired column cell "answer".

2. Enter the number corresponding to the number of the correct answer.

3. Click the Enter key.

Test on the topic "Decision of triangles"

Option 1

In tasks №1-4, select the correct answer and bring it into the table on the sheet1, clicking the LKM on the sheet tab1 in the lower left corner of the screen.

In the triangle ABC AB \u003d Sun \u003d 2. If acosb \u003d - 1/8, then the side of the ACequal to:

1) √ 7

2) 7

3) 3

4) 9

In the triangle ABC side AB \u003d 3, the side of the AC \u003d 5. Then the attitude (sIN B) :( SIN C) Equally:

1) 5 / 3

2) 3 / 5

3) 4 / 5

4) 5 / 4

In the rectangular triangle AVS angle C \u003d 45 0 . If av \u003d 4, then the hypotenuse of the sunequal to:

1) 8

2) 4√ 3

3) 2√ 2

4) 4√ 2

In the triangle ABC AV \u003d 2, Sun \u003d 3. If the angle is \u003d 36 0, then

1) angle in stupid

2) corner in direct

3) angle in acute

4) Corner type in install can not

Auellbekova Gavhar Diembekovna

Lyceum at Kazgas

Question 1: Select the correct formulation of the definition of a rectangular triangle:

Triangle, who has only two sharp corners

Triangle with straight sides

Triangle, who has all the corners direct

A triangle who has one corner straight, and two other sharp

Question 2: What is the name of the side of the rectangular triangle, opposing the straight corner?

Base

Cathe

Hypotenuse

Difficult to answer

Question 3: Continue the wording:

If the sharp corner of the rectangular triangle is 30 °, then ...

katat is equal to half of the hypotenuse

hypotenus is equal to cathetua

roots, lying against this angle, is equal to half of the hypotenuse

hypotenuse more category

Question 4:

What triangle is called Egyptian? What is equal

cOS 45 °?

Question 5:

In the triangle ABC (  C \u003d 90 °)  A \u003d 30 °, sun \u003d 12 cm

Find the length of the AV hypotenuse.

6 cm

12cm

24 cm

Cannot be determined

Question 6: In an equally chained triangle ABC with the base of the aircraft, the height of the AD was carried out.

Find the values \u200b\u200bof the corners in and c if

side side of the triangle ac \u003d 7 cm, and Cd \u003d 3.5 cm

Cannot be determined

Question 7: In a rectangular, ancobed triangle of hypotenuse is 18 cm. Determine the height of the triangle, lowered from the vertex of the straight angle.

Cannot be determined

You worked well !

Getting to solve the following task .

Repeat theory again and come back to the task.