Congruence of Triangles By ASA Criteria
Congruence of Triangles by ASA Criteria
Theorem: Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.
Given: , in which
To Prove:
Proof: On comparing the sides AC and DE of , there are three possibilities:
(i) AC = DE (II) AC < DE (iii) AC > DE
|
Case (i): when AC = DE, then in AC = DE [ Assumed]
CB = EF [Given] Hence, |
 |
|
Case (ii) : When AC < DE, then we take point G on DE such that AC = GE , Join GF Now in AC = GE [ Assumed] CB = EF [ Given ]
Hence, Hence But Therefore From (1) and (2) we get Therefore AC = DE , Hence |
 |
Case (iii): When AC > DE, then we take point G on AC such that GC = DE
Then as in Case (ii) we can prove that A coincide with G i.e. AC = DE, Hence [ By SAS Criterion]
Hence in all the three cases
Illustration: AB is a line segment, AX and BY are two equal line segments drawn on opposite sides of line AB such that . If AB and XY intersect each other at P , prove that
(i) (ii) AB and XY bisect each other.
|
Solution: Since Similarly, we have BY at X and Y respectively] Thus, in triangles PAX and PBY, we have and, AX = BY So, by ASA congruence criterion, we have
Hence, |
 |
Illustration: AB is line segment and P is its mid - point. D and E are points on the same side of AB such that
BAD =
ABE and
EPA =
DPB.Show that
(i) DAP
EBP
(ii) AD = BE
Solution:
Given: AB is a line segment and P is its mid - points. D and E are points on the same side of AB such that BAD =
EPA =
DPB.
Prove that : (i) DAP
EBP
(ii) AD = BE
Proof: (i) Since, P is the mid - point of the line segment AB
In
DAP and
EBP,
AP = BP
Also, given DAP =
EBP
and EPA =
DPB
Adding EPD to both sides
EPA +
EPD =
EPD +
DPB
APD =
BPE
Thus, by ASA rule
DAP
EBP
(ii) Since, DAP
EBP (From above)
AD = BE (CPCT)
In the figure given below,
| |||
| Right Option : B | |||
| View Explanation | |||
â–³ABC and â–³PQR are congruent under the correspondence ABC ↔ RQP. Write the parts of ΔABC that correspond to RP. | |||
| Right Option : A | |||
| View Explanation | |||
If | |||
| Right Option : B | |||
| View Explanation | |||
Students / Parents Reviews [10]
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.
Ayan Ghosh
8thMy 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.
Hiya Gupta
8thIt 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
Barkha Arora
10thMy 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.
Shivam Rana
7thAbhyas 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.
Om Umang
10thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thOne 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.
Aman Kumar Shrivastava
10thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thIt 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.
Cheshta
10thIt 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.
