Converse of Midpoint Theorem

Q.

Given six line segments of length $2,3,4,5,6,7$units, the number of triangles that can be formed by these lines is?

1. ${}^{6}C_3-7$

2. ${}^{6}C_3-6$

3. ${}^{6}C_3-5$

4. ${}^{6}C_3-4$

Q. t is given that ∠XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

Q. Which of the following states that, "If a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side" ?

1. Basic proportionality theorem
2. Midpoint theorem
3. Converse of midpoint theorem
4. Pythagorean Theorem

Q.

In the given figure, ABCP is a parallelogram and P is the mid point of CD. Then find which of the following option is correct?

1. $OB=\frac{1}{2}BD$
2. $AP=\frac{1}{2}BC$
3. $PD=AP$
4. $OA=\frac{1}{2}CD$

Q.

In a triangle $ABC$, $D$ is the midpoint of $AB$ and $E$ is a point on $AC$ such that $DE||BC$. Then

1. AE=EC

2. AE= AC/2

3. Neither of the above

4. Both of the above

Q.

The diagonals of parallelogram ……

1. are congruent

2. are perpendicular

3. bisect each other

4. rectangle

Q. Diagonals of a parallelogram bisect each other.

1. True
2. False

Q.

In the given figure, D is the mid-point of AB and $PC=\frac{1}{2}AP=3$ cm. If $AD=DB=4$ cm and $DE||BP$ , then AE is

1. 8 cm

2. 3 cm

3. 5 cm

4. 4 cm

Q. When we formally prove the angle sum property of a triangle then we need to draw a line parallel to the base of triangle.. why this is so?any particular reason??

Q. In a parallelogram, opposite angles are supplementary.

1. False
2. True

Q.

In a triangle $ABC$, $D$ is the midpoint of $AB$ and $E$ is a point on $AC$ such that $DE||BC$. Then

1. AE=EC

2. Both of the above

3. Neither of the above

4. AE= AC/2

Q. In the given figure, D is the mid-point of ABand $PC=\frac{1}{2}AP=3$ cm. If $AD=DB=4$ cm and $DE||BP$ , then AE is

1. 3 cm
2. 5 cm
3. 8 cm
4. 4 cm

Q. ABC is a triangle. If DE || BC and $DE=2\times BC$, then burst the correct equalities.

1. AD = DB
2. AD = AB
3. $AD=2\times AB$
4. AE = AC
5. AE = EC
6. $AE=2\times AC$
7. ∠ADE = ∠ABC
8. ∠AED+∠ACB
   = 180°

Q. Assertion : ABCD and PQRC are rectangles and Q is mid - point of AC. Then DP = PC.

Reason : The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it.
Which of the following is correct?

1. If both assertion and reason are true and reason is the correct explanation of assertion
2. If both assertion and reason are true but reason is not the correct explanation of assertion
3. If assertion is true but reason is false
4. If assertion is false but reason is true

Q. Which of the following states that, "If a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side" ?

1. Basic proportionality theorem
2. Midpoint theorem
3. Converse of midpoint theorem
4. Pythagorean Theorem

Q. The line segment joining the mid - points of any two sides of a triangle is parallel to the third side and equal to half of it.
In the given figure, the side AC of $\Delta ABC$ is produced of E such that $CE=\frac{1}{2}AC$. If D is the mid - points of BC and ED produced meets AB at F and CP, DQ are drawn parallel to BA, then FD =

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