# Congruency Criterion for Triangles AAS, ASA, SSS, SAS

## Trending Questions

**Q.**

Prove the converse of mid-point theorem.

**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.

**Q.**

**Question 7 (iii)**

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, Show that:

ar(ΔPBQ)=ar(ΔARC).

**Q.**

If △ABC ≅ △DEF by SSS congruence, then, which of the following options is correct?

AB = DE, BC = FE, CA = FD

AB = DE, BC = FE, C = F

AB = FD, BC = DE, CA = FE

AB = EF, BC = FD, CA = DE

**Q.**Each diagonal of a parallelogram divides it into two congruent triangles.

- False
- True

**Q.**In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F,

Show that ar(BDE)=12ar(BAE)

**Q.**D, E, and F are respectively the mid-points of the sides AB, BC and CA of a ΔABC. Triangles are formed by joining these mid-points D, E and F. Which among the following is true?

- ΔEFD≅ΔCFE
- ΔDEF≅ΔEDB
- All the above
- ΔADF≅ΔEFD

**Q.**The opposite sides of a parallelogram are equal is proved using the postulate

- ASA
- SSS
- SAS

**Q.**

**Question 5 (iii)**

In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that:

(iii) ar(ABC) = 2ar(BEC)

**Q.**I chapter 9 their is a theorem 1 known as parallelogram on the same Base and between the Same parallel are equal in area in ncert book of class 9 this theorem is proved by using ASA but in byjus it is proved by AAS which solution is right

**Q.**

D, E, and F are respectively the mid-points of the sides AB, BC and CA of a ΔABC. Triangles are formed by joining these mid-points D, E and F. Which among the following is true?

All the above

ΔDEF≅ΔEDB

ΔEFD≅ΔCFE

ΔADF≅ΔEFD

**Q.**P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP,

Show that ar(ΔPBQ)=ar(ΔARC).

**Q.**

**Question 5 (ii)**

In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F,

Show that: ar(BDE)=12ar(BAE)

**Q.**

**Question 5 (iv)**

In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that:

(iv) ar(BFE) = ar(AFD)

**Q.**Question 7 (iii)

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that

CM=MA=12AB .

**Q.**The side AC of a triangle ABC is produced to E so that CE = 1/2 AC .D is the midpoint of BC and ED produced meets AB at F .Lines through D and C are drawn parallel to AB which meet AC at P and EF at point R respectively. prove that:

1) 3DF = EF

2) 4CR = AB

**Q.**Each diagonal of a parallelogram divides it into two congruent triangles.

- False
- True

**Q.**Let X be any point on the side BC of a triangle ABC. If XM, XN are drawn parallel to BA and CA meeting CA, BA in M, N respectively. MN meets CB produced in T. Then

- TB2=TX×TC
- TC2=TB×TX
- TX2=TB×TC
- TX2=2(TB×TC)

**Q.**

In the parallelogram, D is the mid point of side PQ. Which of the following options is NOT true?

PD = RS

DQ = RS

All of the above

PQ = RS