Congruent Figures
Trending Questions
Q. If ΔXYZ and ΔABC are congruent, then which of the following is false?
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/77402/content_2.jpg)
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/77402/content_2.jpg)
- XY = AB, YZ = BC and ZX = AC
- Both the triangles can overlap
- Area(ΔABC) = Area(ΔXYZ)
- All of these
Q. The medians of a triangle ABC intersect at G.
To show: Area (ΔAGB)=13 Area (ΔABC)
To show: Area (ΔAGB)=13 Area (ΔABC)
Q. Question 2
In a triangle ABC, E is the mid-point of the median AD.
Show that ar(ΔBED)=14ar(ΔABC)
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_36addf93144ebc4345b4b05af1980a13b444be8f20160919-20734-118ezt0.png)
In a triangle ABC, E is the mid-point of the median AD.
Show that ar(ΔBED)=14ar(ΔABC)
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_36addf93144ebc4345b4b05af1980a13b444be8f20160919-20734-118ezt0.png)
Q. Question 4
‘If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent; Is the statement true? Why?
‘If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent; Is the statement true? Why?
Q. D, E and F are respectively the mid-points of the sides AB, BC and CA of a ΔABC. Prove that by joining these mid-points D, E and F, the ΔABC is divided into four congruent triangles.
Q. Which of the following statement is correct for congruent triangles?
- Congruent triangles have same shape but different size.
- Congruent triangles have neither same shape nor same size.
- Corresponding angles and corresponding sides of congruent triangles are equal.
- Congruent triangles have same size but different shape.
Q. ABC and ABD are two triangles on the same base AB. If line-segment CD is bisected by AB at O, show that ar(ABC)=ar(ABD).
![1300026_ceb85f5832e44768addca181ce5bc9d6.PNG](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/1300026_ceb85f5832e44768addca181ce5bc9d6.PNG)
Q. Question 16
D, E and F are respectively the mid-points of the sides AB, BC and CA of a ΔABC. Prove that by joining these mid-points D, E and F, the ΔABC is divided into four congruent triangles.
D, E and F are respectively the mid-points of the sides AB, BC and CA of a ΔABC. Prove that by joining these mid-points D, E and F, the ΔABC is divided into four congruent triangles.
Q. D, E and F are respectively the mid-points of the sides AB, BC and CA of a ΔABC. Prove that by joining these mid-points D, E and F, the ΔABC is divided into four congruent triangles.
Q.
Show that a median of a triangle divides it into two triangles of equal areas. [3 MARKS]
Q. Prove that perimeter of a triangle is greater than sum of its three medians.
![514542_6e1d5fe4dbe74587afd5ae5ca34f8903.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/514542_6e1d5fe4dbe74587afd5ae5ca34f8903.png)
![514542_6e1d5fe4dbe74587afd5ae5ca34f8903.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/514542_6e1d5fe4dbe74587afd5ae5ca34f8903.png)
Q. In △ABC, AB=AC and AD is perpendicular to BC. State the property by which △ADB≅△ADC.
- SAS property
- SSS property
- RHS property
- ASA property
Q. Two line segments are congruent if _____________.
Q.
The theorem which describes "Two angles and the included side of two triangles are congruent" is:
A.A.S.
S.A.S.
A.S.A.
S.S.S.
Q.
In the given figure, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar (ACE) [2 MARKS]
Q. Select the alternative which correctly depicts how a paper will appear, when it is folded along the dotted line?
![350695.PNG](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/350695.PNG)
- A
- B
- C
- D
Q. Which of the following condition even if satisfied, does not make the two triangles congruent?
- S.S.S ( side-side-side)
- A.A.A (angle-angle-angle)
- S.A.S (side-angle-side)
- A.S.A (angle-side-angle)
Q.
Prove that any two sides of a triangle are together greater than twice the median drawn to the third side. [4 MARKS]
Q. In ΔABC, D is the mid-point of BC. Name the line segment AL and AD.
![1297515_ad9d5b39db8d427096773f1b8e2d94cb.png](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/1297515_ad9d5b39db8d427096773f1b8e2d94cb.png)
![1297515_ad9d5b39db8d427096773f1b8e2d94cb.png](https://search-static.byjusweb.com/question-images/toppr_invalid/questions/1297515_ad9d5b39db8d427096773f1b8e2d94cb.png)