### Common Errors in Secondary Mathematics

Common Errors Committed  by the  Students  in Secondary Mathematics   Errors  that students often make in doing secondary mathematics  during their practice and during the examinations  and their remedial measures are well explained here stp by step.  Some Common Errors in Mathematics

### Lesson Plan Math Class X (Ch-6) | Triangles

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10
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 TEACHER'S NAME  :  Dinesh Kumar SCHOOL : RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR SUBJECT   :   MATHEMATICS CLASS                  :   X  STANDARDBOARD                 :  CBSE LESSON TOPIC / TITLE   : CHAPTER 06: SIMILARITY OF TRIANGLES ESTIMATED DURATION: This chapter is divided into seven modules and it is completed in twenty class meetings.

PRE- REQUISITE KNOWLEDGE:-
Knowledge of congruent figures,

TEACHING AIDS:-
Green Board, Chalk,  Duster, Charts, smart board, laptop, projector  etc.

METHODOLOGY:-
Demonstration and Lecture method.

LEARNING OBJECTIVES
• Definitions, examples and counter examples of similar of triangles.
• Prove : If a line is drawn parallel to one side of the triangle to intersect the other two sides at two distinct points the other two sides are divided in the same ratio or
• Motivate : If a line intersect the two sides of the triangle in the same ratio,  the line is parallel to the third side.
• Motivate: If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
• Motivate: If corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar to each other.
• Motivate: If one angle of a triangle is equal to the one angle of other triangle and the sides including these angles are proportional, the two triangles are similar.
• Motivate: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on either side of the perpendicular are similar to each other and to the whole triangle.
• Prove : The ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
• Prove :In a right triangle, the square on the hypotenuse is equal to the sum of square on the other two sides.
•  Prove :In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the first side is a right angle.
Note: Theorems for motivation will not be asked in the examination. Only the theorems mentioned with prove will be asked in the examinations.

LEARNING OUTCOMES:
After studying this lesson students should learn the
• Difference between similarity and congruency of plane figures.
• Different similarity and congruency conditions.
• Statement and proofs  of B.P.T. Ratio of area of two similar triangles, Pythagoras theorem and the converse of Pythagoras theorem.
• Students should learn the  implementation of these theorems in the different problems.
RESOURCES
NCERT Text book of Mathematics
NCERT Exemplar Text Book
RESOURCE CENTRE at cbsemathematics.com

KEY WORDS :
Similarity, congruency, Median, Orthocenter, Incentre, Altitude, Centroid, etc.
PROCEDURE

Start the session by checking their previous knowledge, by asking the questions of congruence of triangles and its different conditions. After this explain the topic to the students step by step as follows.

Introduction

First of all teacher will show some figures o the students which are looks same but different in size. Now teacher will introduce the concept similarity of figures give definition of similarity of triangles.

With the help of some examples teacher will explain the following to the students

All circles are similar to each other.

All equilateral triangles are similar to each other.

All squares are similar to each other.

All regular polygons with equal sides are similar to each other.

Difference between Similarity and Congruency

Now teacher will explain the difference between the similarity and congruency of the plane figures by giving examples and counter examples.

Basic Proportionality Theorem

Now teacher will write the statement of Basic Proportionality Theorem on the board and explain the meaning of this statement by drawing the figure.

After this teacher will explain the proof of the theorem which include the components: Given, To Prove, Construction, Proof.

After the complete explanation of the BPT teacher will motivate the students for the converse of Basic Proportionality theorem and also give its complete proof.

Now teacher will explain the procedure of implementing these theorems in different problems. Teacher may also provide sufficient number of problems to the students so that the students will completely understand the theorem.

Similarity Conditions

Now teacher will define all similarity conditions (SSS, SAS, AAA, AA)  to the students. Teacher will also motivate the students for the proof of these theorems.

Teacher will explain the implementation of these theorems in different problems.

Define the theorem:

If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on either side of the perpendicular are similar to each other and to the whole triangle. Also motivate the student to learn the proof of this theorem.

Theorem on the area of two similar triangles

State and prove the theorem on the ratio of area of two similar triangle is equal to the ratio of their corresponding sides.

Teacher will explain its proof, which include the following components Given, To Prove, Construction and Proof. Teacher will also assign some problems to the students for the implementation of the theorem.

Pythagoras Theorem

Now teacher will introduce The Pythagoras Theorem.

Teacher will explain the statement of this theorem with the help of a diagram and also explain the complete proof of the theorem which include the following components: Given, To Prove, Construction and Proof.

Teacher will also assign some problems to the student to learn the implementation of this theorem.

Converse of Pythagoras Theorem

Now teacher will introduce The Converse of Pythagoras Theorem.

Teacher will explain the statement of this theorem with the help of diagram and also explain the complete proof of the theorem which include the following components: Given, To Prove, Construction and Proof.

Teacher will also assign some problems to the student to learn the implementation of this theorem.

STUDENTS DELIVERABLES:-
• Review questions given by the teacher.
• Students should made the presentation on any one of the theorem for the proof.
• Solve N.C.E.R.T. problems with examples,
• Solve the assignment on Multiple Choice Question (MCQ) given by the teacher.
EXTENDED LEARNING:-
Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts on mathematics at  cbsemathematics.com

ASSESSMENT TECHNIQUES
Assignment sheet will be given as home work at the end of the topic. Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
Class Test , Oral Test , worksheet and Assignments can be made the part of assessment.
Re-test(s) will be conducted on the basis of the performance of the students in the test.

FEEDBACK:
All those students who performed well will be appreciated positively, and all those who can not perform up to the mark will again be given some important tips, guidance and  positive motivation to go through the topic again and then re-evaluated again. If possible then provision of remedial classes can be made for batter results.

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