Subject Mathematics Geometry Total 68 hours

Theme of the lecture Phales Theorem 2 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Grade 8 Academic year 2014-2015 2 term

Lesson 13,14

Statement of theorem

If parallel lines cross one side of angle and cut equal segments, then they cut equal segments on the other side too.

Proof

Lets A_1, A₂, A₃ – points of crossing parallel lines with one side of angle. Lets denote B₁, B₂, B₃ corresponding points of crossing this lines with another side of angle. Prove that if A₁A₂=A₂A₃ than respectively B₁B₂= B₂B₃. Lets draw through point B₂ straight line of FE parallel to A₁A₂. According to the property of the parallelogram A₁A₂=FB₂, A₂A₃=B₂E. So if A₁A₂=A₂A₃ than FB₂=B₂E. Triangles B₁B₂F and B₂B₃E are equal according to the second test of equality. Really B₂F=B₂E, angles FB₂B₁=B₃B₂E as vertical angles, angles B₂FB₁ and B₂EB₃ are equal as interior alternate angles at parallel lines A₁B₁ and A₃B₃ and crossing line FE. From the equality of triangles B₂B₁F and B₂B₃F we can say that B₁B₂=B₂B₃. The theorem proved.

Task 1:

Divide segment into definite number of parts.

Glossary

Home task Lesson 1 task 128, 129 Lesson 1 task 132,133

Individual work of student: Collection for preparing to examination Group 15 (15B21 –15B22).

Office–hours Geometry 8grade Шыныбеков А.Н., 2012, ex 35 ( p 33-37)

Literature: Geometry 8grade Шыныбеков А.Н. 2012, [33-37], 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 Trapeze 2 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Grade 8 Academic year 2014-2015 1 term

Lesson 15-17

Definition

Trapeze – quadrilateral in which two opposite sides are parallel and called bases., not parallel sides are called lateral sides

AB, CD- lateral sides. BC,AD- bases.

Definition

Rectangular trapeze – trapeze in which one angle is right angle.

BAD= 90⁰

Definition

Isosceles trapeze – is trapeze in which lateral sides are equal.

AB=CD

Definition

Middle line in trapeze – is a line which joins middle of lateral sides.

EF- middle line.

Theorem

Middle line in trapeze is parallel to the base and equal to the half of sum of the bases.

Prove

ABCD – trapeze. EF – midline. Lets draw through the vertex B and point F - midpoint of lateral side CD straight line CD.

Lets this straight line crosses straight line AD in the point P. So we get two equal triangles. Triangle BFC and triangle PFD are equal according to the second test of equality of triangles, because CF = FD, CFB = DFP, as vertical, BCF = PDF as alternate interior angle with parallel lines BC, DP and secant line CD.

From the equality of this triangles we write the equality of sides BF = FP. So EF is midline of triangle ABP. According to the property of midline of triangle, EF is parallel to the AD so it is parallel and BC too.

EF = AP because BC = DP and AP = AD + DP, then EF = ( AD + BC).

The theorem proved.

Task

Middle line in trapeze is 8 cm, one base is 6 cm. Find another base.

Glossary

Home task Theorem, definitions

Lesson 1 ex 150 ,153 Lesson 2 ex 154, 155 Lesson 3 ex 163, 164

Individual work of student: Collec. for preparing to examination Group 15 (15B25 –15B26).

Office–hours Geometry 8grade Шыныбеков А.Н. 2011, ex 102,101 ( p 37- 42)

Literature: Geometry 8grade Шыныбеков А.Н. 2011, [37- 42], Collection for preparing to examination Group15

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

Notes

Kazakh-American University