Similarity of Triangles by AAA Criteria:
Theorem : If in two triangles, the corresponding angles are equal, then the corresponding sides are proportional ( i.e., in the same ratio) and hence the triangles are similar.
Given: in ABC and DEF
To Prove :
Construction: Cut DP = Ab and DQ = Ac and Join PQ. Proof: In ABC and DPQ AB = DP [ By Construction ] A = D [ Given] AC = DQ [ By Construction ] Hence ABC DPQ [ By SAS Criteria] B = P and C = Q [C.P. C. T] But B = E [ Given] Hence P = E But they are corresponding angles when PQ and EF are straight lines and Transversal DE cuts them. As they are equal So the lines are parallel Therefore by Basic Proportionality Theorem
Taking Reciprocal both Sides and adding 1 to both sides we get Taking Reciprocal we get replacing DP with AB and DQ with AC as they are equal by construction We get Similary We can prove that And Hence |
Illustration : If AB || CD , prove that Solution: As AB || CD then [ Alternate Interior Angle ] [ Alternate Interior Angle ] [ Vertically Opposite Angle ] Therefore, [ AAA Similarity Criterion] |
In the following figure, . Then by ________________________ criteria. | |||
Right Option : A | |||
View Explanation |
In the above figure, if and AB || DC. Then the two triangles i.e. AOB and COD are similar by ________________ criteria. | |||
Right Option : A | |||
View Explanation |
In above figure, by __________________ criteria. | |||
Right Option : D | |||
View Explanation |
Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.