Parallel Lines and Transversals

Q.

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

Q.

In the figure, 2 AD = AB, P is the mid point of AB, Q is mid point of DR and $PR\parallel BS$. Then, $\frac{DS}{RS}=$

1. AB AP

2. AB < AP

3. AB > AP

4. AB = AP

Q. In figure, points X, Y, Z are the midpoints of side AB, side BC and side AC of ABC respectively. AB = 5 cm, AC = 9 cm and BC = 11 cm. Find the length of XY, YZ, XZ.

Q. Use the information, given in the adjoining figure, to show that AB = AC

Q. In the given figure, if $AB||CD,\angle APQ={50}^{\circ }$ and $\angle PRD={127}^{\circ }$, the value of y is

1. 77

Q.

In the given figure, AP = AQ and the right agles are shown. Which of the following statements can certainly be stated?

1. AP = PB

2. AB = AC

3. AQ = AD

4. None of these