Converse of Pythagoras Theorem by Contradiction

Q.

Assertion: In $\Delta ABC$, E and F are the mid-points of AC and AB respectively. The altitude AP at BC intersect and FE at Q. Then AQ = QP.
Reason: Q is the mid - point of AP.
Which of the following is correct?

1. Both the assertion and the reason are true and the reason is the correct explanation for the assertion
2. Both the assertion and the reason are true but the reason is not the correct explanation for the assertion
3. The assertion is true and the reason is false
4. The assertion is false and the reason is true

Q.

In the given figure, $AD$ is a median of $△ABC$ and $E$ is the mid-point of $AD.$ Also, $BE$ produced meets $AC$ in $F.$ Then $AF=$

1. $\frac{1}{2}AC$

2. $3AC$

3. $2AC$

4. $\frac{1}{3}AC$

Q. Triangle ABC is 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. In the given figure, AD is a median of ABC and E is the mid-points of AD. Also, BE produced meets AC in F. Then AF =

1. $\frac{1}{3}AC$
2. $2AC$
3. $\frac{1}{2}AC$
4. $3AC$

Q. In the given figure, M, N, and P are the mid-points of AB, AC, and BC, respectively. If MN = 3 cm, NP = 3.5 cm, and MP = 2.5 cm, find the perimeter of the triangle ABC (in cm).

Q.

Assertion: In $\Delta ABC$, E and F are the mid-points of AC and AB respectively. The altitude AP at BC intersect and FE at Q. Then AQ = QP.
Reason: Q is the mid - point of AP.
Which of the following is correct?

1. Both the assertion and the reason are true and the reason is the correct explanation for the assertion
2. Both the assertion and the reason are true but the reason is not the correct explanation for the assertion
3. The assertion is true and the reason is false
4. The assertion is false and the reason is true

Q.

Assertion: In $\Delta ABC$, E and F are the mid-points of AC and AB respectively. The altitude AP at BC intersect and FE at Q. Then AQ = QP.
Reason: Q is the mid - point of AP.
Which of the following is correct?

1. Both the assertion and the reason are true and the reason is the correct explanation for the assertion
2. Both the assertion and the reason are true but the reason is not the correct explanation for the assertion
3. The assertion is true and the reason is false
4. The assertion is false and the reason is true

Q. Triangle ABC is 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. In the given figure, AD is a median of ABC and E is the mid-points of AD. Also, BE produced meets AC in F. Then AF =

1. $3AC$
2. $\frac{1}{2}AC$
3. $2AC$
4. $\frac{1}{3}AC$

Q. In the given figure, AD is a median of ABC and E is the mid-points of AD. Also, BE produced meets AC in F. Then AF =

1. $3AC$
2. $\frac{1}{2}AC$
3. $2AC$
4. $\frac{1}{3}AC$