Hello students. I am going to tell you about Geometric proofs in Grade XII of Karnataka board syllabus for various shapes like triangles, circles and many more. Geometry considers all the measurements of a figure like shape, size, and associate position of figures. Geometric proofs are the step by step process from postulates of a proof to outcomes. There are two most approaches that works for proofs of geometry. They are direct proof and indirect proof. Subsidiary lines are draft along with the proofs. Also improve your knowledge in Introduction to geometry.
For geometric proofs you have to follow some terms that are used frequently. They are:
-Auxiliary lines:-Created to provide support to assure statement.
-Contradiction:- This case arises when the negation of a true expressions is also true.
-Direct proof:- In this we can directly take conclusion from the antecedent conclusions.
-Indirect proof:- When it follows contradiction.
-Paragraph proof:-In this proof we can written all steps into single expression in a paragraph form.
-Two columns proof:-In this type of proof we construct a two column table the first column consist all conclusion and second column consist the reasons for each conclusion.
-Geometric proof:- It is a step by step procedure that used all of the terms.
Note:- paragraph and two column proof are not same although they have same in content.
I am giving you a geometric proofs example so that you can understand it in a better way:-
We have a figure:
in given figure Section PR intersect SQ
Section QS intersect RP.
So you need to prove triangle PQZ and RSZ are congruent.
In upcoming posts we will discuss about Intersection of a plane with 3-d figures and dispersion. Visit our website for information on Area of a Circle Formula
For geometric proofs you have to follow some terms that are used frequently. They are:
-Auxiliary lines:-Created to provide support to assure statement.
-Contradiction:- This case arises when the negation of a true expressions is also true.
-Direct proof:- In this we can directly take conclusion from the antecedent conclusions.
-Indirect proof:- When it follows contradiction.
-Paragraph proof:-In this proof we can written all steps into single expression in a paragraph form.
-Two columns proof:-In this type of proof we construct a two column table the first column consist all conclusion and second column consist the reasons for each conclusion.
-Geometric proof:- It is a step by step procedure that used all of the terms.
Note:- paragraph and two column proof are not same although they have same in content.
I am giving you a geometric proofs example so that you can understand it in a better way:-
We have a figure:
in given figure Section PR intersect SQ
Section QS intersect RP.
So you need to prove triangle PQZ and RSZ are congruent.
| Statements | Reasons |
| 1.Section PR intersect SQ. | 1.Given |
| 2.Sections PZ and RZ are congruent. | 2.When a section is intersected then two resulting section are congruent. |
| 3. Section QS intersect RP. | 3.Given |
| 4. Sections QZ and SZ are congruent. | 4. When a section is intersected then two resulting section are congruent |
| 5.Angles PZQ and RZS are congruent. | 5.Verticals angles are congruent. |
| 6.Triangles PQZ and RSZ are congruent | 6.SAS postulates. |
In upcoming posts we will discuss about Intersection of a plane with 3-d figures and dispersion. Visit our website for information on Area of a Circle Formula
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