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Subject Mathematics Geometry Total 68 hours

Kazakh-American University

Subject Mathematics Geometry Total 68 hours

Theme of the lecture Quadrilateral 2 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Lesson 5

Definition:

Quadrilateral is a figure, which consists of four point and four segments joint consequently. Four points don’t belong to one straight line.

If number of points is more than four- this figure is called polygon.

A, B and B,C and C,D and D,A- adjacent vertexes;

A, RegularC and B,D- opposite vertexes;

A, B, C, D or ABC, BCD, CDA, DAB- angles of quadrilateral;

AC and BD- diagonals of quadrilateral.

Perimeter of quadrilateral is sum of length of all sides. Quadrilateral divides plane in two parts: interior and exterior.

Convex quadrilateral- if each angle is less than two right angles.

Regular or Equilateral quadrilateral – if all sides are equal to each other.

Exercises:

Prove that some of angles of quadrilateral is equal to 3600

Glossary

 English Russian Kazakh Quadrilateral Четырехугольник Төртбұрыш Vertex Вершина Төбесі Convex Выпуклый Дөңес Angle Угол Бұрыш Square Квадрат Квадрат Rhomb Ромб Ромб

Lesson 1 ex 28,29, 30

Individual work of student: Collection for preparing to examination Group 15 (15A01 –15A05).

Office–hours Geometry 8grade Шыныбеков А.Н. 2011, ex 7 ( p 3-5)

Literature: Geometry 8grade Шыныбеков А.Н. 2011, [3 – 5], Collection for preparing to examination Group15

Notes

Kazakh-American University

Subject Mathematics Geometry Total 68 hours

Theme of the lecture Parallelogram 2 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Lesson 6-8

Definition

Two segments are called parallel if they belong to parallel lines.

Definition

Parallelogram – quadrilateral in which opposite sides are parallel

Tests for parallelogram

1. Opposite sides are equal

2. Point of crossing of diagonals divides them in half

3. Opposite side are parallel and equal

Theorem

If two opposite sides of quadrilateral are equal and parallel, this quadrilateral is parallelogram

Theorem

If opposite angles of quadrilateral are equal then this quadrilateral is parallelogram

Theorem

If point of crossing of diagonals of quadrilateral divides them in half, then this quadrilateral is parallelogram

1. How many questions is it possible to construct using two equilateral triangles

2. How many questions is it possible to construct using two isosceles triangles

3. How many questions is it possible to construct using two arbitrary triangles

Glossary

 English Russian Kazakh Quadrilateral Четырехугольник Төртбұрыш Vertex Вершина Төбесі Convex Выпуклый Дөңес Angle Угол Бұрыш Square Квадрат Квадрат Rhomb Ромб Ромб

Lesson 1 ex 53, 54. Lesson 2 ex 57, 59

Lesson 3 ex 62, 63

Individual work of student: Collection for preparing to examination Group 15 (15A06 –15A10).

Office–hours Geometry 8grade Шыныбеков А.Н. 2012, ex 11, 20 ( p 5-8)

Literature: Geometry 8grade Шыныбеков А.Н. 2012, [5- 8], Collection for preparing to examination Group15

Notes

Kazakh-American University

Subject Mathematics Geometry Total 68 hours

Theme of the lecture Rectangle 2 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Lesson 9

Definition

Rectangle - is a quadrilateral in which each angle is equal to right angle.

Properties of rectangle

Rectangle – is a parallelogram with equal angles. Diagonals of rectangle are equal.

Rectangle has all properties of parallelogram.

Write all properties of rectangle, using properties of parallelogram.

Glossary

 English Russian Kazakh Quadrilateral Четырехугольник Төртбұрыш Vertex Вершина Төбесі Convex Выпуклый Дөңес Angle Угол Бұрыш Square Квадрат Квадрат Rhomb Ромб Ромб

Lesson 1 ex 87, 88

Individual work of student: Collection for preparing to examination Group 15 (15A10 –15A15).

Office–hours Geometry 8grade Шыныбеков А.Н. 2011, ex 11, 20 ( p 21-33)

Literature: Geometry 8grade Шыныбеков А.Н. 2011, [21 - 33], Collection for preparing to examination Group15

Notes

Kazakh-American University

Subject Mathematics Geometry Total 68 hours

Theme of the lecture Rhomb. Square 2 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Lesson 10 – 11

Lesson 12 – Control work

Definition

Rhomb – is a parallelogram with equal sides

Properties of rhomb

All side are equal

Opposite angles are equal

Point of crossing of diagonals divides them in half

Diagonals of rhomb are perpendicular to each other

Diagonals are bisectors of their angles.

Definition

Square – is a rectangle with equal sides

Properties of square

All sides are equal

Each angle is equal to right angle

Diagonals are equal

Point of crossing of diagonals divides them in half

Diagonals are bisectors of each angle

Diagonals are perpendicular to each other

Solve problem

Find perimeter of rectangle if bisector of angle A divides angle side BC in segments 45,6 cm and 7,885 cm.

Glossary

 English Russian Kazakh Quadrilateral Четырехугольник Төртбұрыш Vertex Вершина Төбесі Convex Выпуклый Дөңес Angle Угол Бұрыш Square Квадрат Квадрат Rhomb Ромб Ромб

Home task Lesson 1 ex 97, 98 Lesson 2 ex 101, ex 102

Individual work of student: Collection for preparing to examination Group 15 (15A16 –15A20).

Office–hours Geometry 8grade Шыныбеков А.Н. 2011, ex 21, 28 ( p 921-33)

Literature: Geometry 8grade Becboev Zh, 2012, [21-33], Collection for preparing to examination Group15

200]

Notes

Kazakh-American University

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