AAS Criteria for Congruency
Trending Questions
Q. In the below figure, if ΔABE≅ΔACD, show that ΔADE∼ΔABC.
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_f5184427d18fa91b67b9ed990258837e72f72bd120160911-20462-1lzk0vg.png)
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_f5184427d18fa91b67b9ed990258837e72f72bd120160911-20462-1lzk0vg.png)
Q.
In the given figure, RS = QT and QS = RT. Then which of the following options is correct?
PQ=PR
PQ=QS
none of these
PR=TR
Q.
In △ABC, the ratio of altitudes BE and CF is equal to one. What can be said about the nature of △ABC?
Isoceles
Equilateral
Scalene
Data not enough
Q.
Which of the following cannot be used to prove the congruency of 2 triangles?
SAS
SSS
AAA
RHS
Q. In the below figure, if ΔABE≅ΔACD, show that ΔADE∼ΔABC.
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_f5184427d18fa91b67b9ed990258837e72f72bd120160911-20462-1lzk0vg.png)
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_f5184427d18fa91b67b9ed990258837e72f72bd120160911-20462-1lzk0vg.png)
Q.
In a pentagon ABCDE, AB=AE, BC=ED and ∠ABC=∠AED, then
State true or false:
∠BCD=∠EDC
- True
- False
Q. In the following figure, E is a point on side CB produced, of an isosceles triangle ABC, with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ΔABD∼ΔECF.
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_8b65f04e252f1999e72a12987b37f154ec45c0b520160911-20462-18wndhe.png)
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_8b65f04e252f1999e72a12987b37f154ec45c0b520160911-20462-18wndhe.png)
Q. ![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/37047/content_tan_inv_root_2.jpg)
ΔQST and ΔQUT congruent to each other by criterion.
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/37047/content_tan_inv_root_2.jpg)
ΔQST and ΔQUT congruent to each other by
- SSS
- ASA
- AAS
Q. In the given figure, ∠ABC = ∠BMC = 90°, AB = 3 m,
BC = 4 m, and AC = 5 m. Find the length of side BM.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1713769/original_6.png)
BC = 4 m, and AC = 5 m. Find the length of side BM.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1713769/original_6.png)
Q.
The sides PQ, PR of ΔPQR are equal, and S, T are points on PR, PQ such that ∠PSQ and ∠PTR are right angles. Hence, ΔPTR≅ΔPSQ
State whether the above statement is true or false.
- True
- False
Q. If two altitudes of a triangle are equal in length, then the triangle is
- right angled
- isosceles
- equilateral
- scalene
Q. In the figure shown DE∥BC and AD=3x−2, AE=5x−4, BD=7x−5 and CE=5x−3. Therefore, the value of x is
![328641.bmp](https://search-static.byjusweb.com/question-images/toppr_ext/questions/328641.bmp)
![328641.bmp](https://search-static.byjusweb.com/question-images/toppr_ext/questions/328641.bmp)
- Only 1
- Only 710
- 1 or 710
- 107
Q. In a ΔABC, ifAB=BC=CA=2a and AD⊥BC then
![320999_a888485632274bd9881ed78b59a6f9e2.PNG](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/320999_a888485632274bd9881ed78b59a6f9e2.PNG)
- i) AD=a√2
(ii) area (ΔABC)=√5a2 - i) AD=a√2
(ii) area (ΔABC)=√3a3 - i) AD=a√3
(ii) area (ΔABC)=√3a2 is proved - i) AD=a√5
(ii) area (ΔABC)=√5a2
Q. ∠ACB=90o and CD⊥AB, prove that CD2=BD×AD.
![1578839_0895a9b4cd1b459682185f3cb2293710.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/1578839_0895a9b4cd1b459682185f3cb2293710.png)
![1578839_0895a9b4cd1b459682185f3cb2293710.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/1578839_0895a9b4cd1b459682185f3cb2293710.png)
Q. ABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are constructed in sides AC and AB. Find the ratio between the areas of △ABE and △ACD.
- 2:1
- 1:1
- 1:2
- none
Q. ![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/37047/content_tan_inv_root_2.jpg)
ΔQST and ΔQUT congruent to each other by criterion.
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/37047/content_tan_inv_root_2.jpg)
ΔQST and ΔQUT congruent to each other by
- SSS
- ASA
- AAS