Thales and Angle Bisector theorem and Construction of triangles. Mathematics State Board, Class 10: lessons, tests, tasks.

1.	Introduction
2.	Basic proportionality or Thales theorem
3.	Angle bisector theorem and its converse
4.	Types of construction of triangle
5.	Construction of a triangle when its base, vertical angle and median are given
6.	Construction of a triangle when its base, vertical angle and altitude are given
7.	Construction of a triangle if its base, vertical angle and the point on the base are given

1.	Multiple choice question Difficulty: easy	2
2.	Two mark example problems I Difficulty: medium	4
3.	Two mark example problems II Difficulty: medium	2
4.	Two mark exercise problems I Difficulty: medium	2
5.	Two mark exercise problems II Difficulty: medium	4
6.	Two mark exercise problems III Difficulty: medium	0
7.	Five mark example problems I Difficulty: medium	5
8.	Five mark example problems II Difficulty: medium	5
9.	Five mark exercise problems I Difficulty: medium	5
10.	Five mark exercise problems II Difficulty: medium	5
11.	Five mark exercise problems III Difficulty: medium	5
12.	Five mark exercise problems IV Difficulty: medium	0
13.	Five mark exercise problems V Difficulty: medium	0
14.	Five mark exercise problems VI Difficulty: medium	0
15.	Five mark exercise problems VII Difficulty: medium	0
16.	Five mark exercise problems VIII Difficulty: hard	0
17.	Five mark exercise problems IX Difficulty: hard	5
18.	Five mark exercise problems X Difficulty: hard	0
19.	Eight mark example problems I Difficulty: hard	0
20.	Eight mark example problems II Difficulty: hard	0
21.	Eight mark example problems III Difficulty: hard	0
22.	Eight mark exercise problems I Difficulty: hard	0
23.	Eight mark exercise problems II Difficulty: hard	0
24.	Eight mark exercise problems III Difficulty: hard	0
25.	Eight mark exercise problems IV Difficulty: hard	0
26.	Eight mark exercise problems V Difficulty: hard	0
27.	Eight mark example problems VI Difficulty: hard	0

1.	Calculate the side AD of triangle ABC Difficulty: easy	1
2.	Determine the side CB of triangle ABC Difficulty: easy	3
3.	Calculate the value of the variable Difficulty: easy	3
4.	Find the length of AE of triangle ABC Difficulty: easy	3
5.	Determine the value of the variable Difficulty: medium	4
6.	Find the side length of the triangle Difficulty: medium	4
7.	Check whether the lines of the triangle are parallel Difficulty: medium	4
8.	Determine the length of PM Difficulty: medium	4
9.	Calculate the length of PT and VQ Difficulty: medium	4
10.	Check whether CD is the bisector of angle C Difficulty: medium	4
11.	Observe the picture and answer the questions Difficulty: hard	6
12.	Determine the height of the small tree Difficulty: hard	5
13.	Calculate the height of the mother Difficulty: hard	5
14.	Verify the trees are parallel Difficulty: hard	5

1.	Answer the following questions Difficulty: hard	9
2.	Prove the following Difficulty: medium	2

1.

Methodical recommendation

Thales and Angle Bisector theorem and Construction of triangles