Kazakh-American University Subject Mathematics Geometry Total 68 hours

Theme of the lecture Quadrilateral 2 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Grade 8 Academic year 2014-2015 1 term

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,C,D- vertexes; AB,BC,CD,AD- sides; AB, CD and AD,BC-opposite sides;

AB, BC and BC,CD and CD,AD and AD,AB-adjacent sides;

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

Home task Theorem, definitions

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

Additional literature Tulebaeva S.K. Geometry . 8 grade. Collections of problems

Notes

Kazakh-American University Subject Mathematics Geometry Total 68 hours

Theme of the lecture Parallelogram 2 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Grade 8 Academic year 2014-2015 1 term

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

Answer Questions and explain

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