Congruency Criterion for Triangles AAS, ASA, SSS, SAS

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 $\Delta ABC$. Prove that by joining these mid-points D, E and F, the $\Delta ABC$ 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:
$ar\left(\Delta PBQ\right)=ar\left(\Delta ARC\right)$.

Q.

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

1. AB = DE, BC = FE, CA = FD

2. AB = DE, BC = FE, C = F

3. AB = FD, BC = DE, CA = FE

4. AB = EF, BC = FD, CA = DE

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

1. False
2. 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 $ar\left(BDE\right)=\frac{1}{2}ar\left(BAE\right)$

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

1. $\Delta EFD\cong \Delta CFE$
2. $\Delta DEF\cong \Delta EDB$
3. $Alltheabove$
4. $\Delta ADF\cong \Delta EFD$

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

1. ASA
2. SSS
3. 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

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Q.

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

1. All the above

2. $\Delta DEF\cong \Delta EDB$

3. $\Delta EFD\cong \Delta CFE$

4. $\Delta ADF\cong \Delta EFD$

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 $ar\left(\Delta PBQ\right)=ar\left(\Delta ARC\right)$.

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: $ar\left(BDE\right)=\frac{1}{2}ar\left(BAE\right)$

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)

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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
$CM=MA=\frac{1}{2}AB$ .

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.

1. False
2. 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

1. $T{B}^2=TX\times TC$
2. $T{C}^2=TB\times TX$
3. $T{X}^2=TB\times TC$
4. $T{X}^2=2(TB\times TC)$

Q.

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

1. PD = RS

2. DQ = RS

3. All of the above

4. PQ = RS