ppt presentation on theorem 1

7/31/2019 Ppt Presentation on Theorem 1

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PRESENTATIONCONCEPT BASED DELIVERY

Theorem on geometry

BY Ms.Shireen mir

FDC ARF KAMRA


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ESSENTIAL PRIOR KNOWLEDGE

Students should have knowledge of

Triangle

Elements of triangle

Angles

Angle bisector

Concept of correspondence of triangles

Concept of congruency of triangles

Steps to prove geometric theorems

S.A.S postulate


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AIM OF THE LESSON

At the end of the lesson students will

be able to prove that,if two sides of atriangle are congruent,then the anglesopposite to these sides are also

congruent


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INTRODUCTION

Q: What is a three sided close figure

called?Ans: TriangleQ: What are the six basic elements

of a triangle?Ans: Three sidesThree angles


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Contd..

Q: What is an angle?Ans: Two rays with a common endpoint form

an angle.

Q: What is an angle bisector?Ans: A line that divides an angle into two equal

angles is called angle bisector.

A

B

C

O


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Q: What are the steps to prove a theorem?

Ans: (i) Statement

(ii) Figure(iii) Given

(iv) To prove

(v) Construction(vi)Proof

Contd..


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Q. What is meant by postulate?

Ans: Postulate is a fundamental agreement

related to a particular branch of math

Q. What is meant by S.A.S postulate?

Ans: If the measure of two sides and their

included angle of one triangle are

congruent to the correspondingsides and included angle of the other

triangle.It is called S.A.S postulate

Contd..


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Continued.

Q. Define geometrical theorem?

Ans. The theorem which can be provedwith the help of the princples of geometry.


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DEVELOPMENT

Concept:

Theorem on geometry

DLO:

The students will be able to prove that,If

two sides of a triangle are congruent.Thenthe angles opposite to these sides are alsocongruent.


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PROCEDURE AND TREATMENT

One of the student will be asked to read

the statement of the theorem.

If two sides of a triangle are congruent,

Then the angles opposite to these sidesare also congruent


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If two sides of a triangle are

congruent,

Then the angles opposite to these

sides are also congruent

GIVEN

TO PROVE

Contd


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Q. What is given part in the statement?

Ans: ABC in which , AB ACQ. Name the opposite angles of these congruent

sides?

Ans. Angle B and Angle C

Ans What is to be proved?

Ans:

A

B C

CB

PROCEDURE AND TREATMENTcontd


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Name the included angle:

YE and ES

ES and YS

YS and YE

Included Angle

SY

E

E

S

Y


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Q. What change has occurred in the figure

after bisection?

Ans: (i)Triangle has divided into twotriangles ABD and ACD

(ii)Angle A has divided intotwo angles

A

B CD

CADBAD ,


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Q. What is the relation between

and ?

Ans: They are congruent

Q. Why they are congruent?

Ans: Because of bisection.

Q. Which side is common in ABD and

ACD?

Ans: Side AD

BAD CAD

A

B CD

Contd..


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Now the teacher will explain the proof of

the theorem by taking correspondence

between these two triangle,A

B CD

AA

B D D C

PROOF


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A

B CD

Statement Reason

ABD ACD

AB AC

CADBAD

Construction

Given

AD AD Common

ABD ACD

CB

S.A.S Postulate

Corresponding angles of congruent

triangles are congruent

PROOF

S

A

S


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EXAMPLES

FROM

DAILY LIFE


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EXAMPLES IN DAILY LIFE


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WOW


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Board summaryGeometrical Theorem

Element of Geometrical Theorem

Statement

Proof

Figure

Given

To Prove

Construction

A


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BOARD SUMMARY

Statements

ABD ACD

AB AC

AD AD

ABD ACD

Reasons

Given

Construction

Common

S.A.S PostulateCorresponding angle ofcongruent triangles arecongruent

CADBAD

CB

A

B CD

A


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RECAPITULATION

Statements

ABD ACD

AB AC

AD AD

ABD ACD

Reasons

Given

Construction

Common

S.A.S PostulateCorresponding angle ofcongruent triangles arecongruent

CADBAD

CB

A

B CD

RECAPITULATION

If h f i b t th


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If you have any confusion about the

topic ,you can ask.


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CONSOLIDATION

Answer the following questions for givenXYZ in which XY XZ

Q. Which angle should be

bisected?

Q. After bisection what new angles

are formed?

Q. Which side is common after bisection?

Q. Which postulate should be used to prove thecongruency of two triangles?

Q. As a result which angles will be congruent?

X

Y

Z


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HOME WORK

Take an isosceles LMNand prove the sametheorem

Submission date:

12- 05-12


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CONCLUSION

Today we have proved that,if two sides

of a triangle are congruent,then the

angles opposite to these sides arealso congruent ,In the next class wewill prove next theorem


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Thank you

ppt presentation on theorem 1

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