# DAV Class 8 Maths Chapter 10 Worksheet 2 Solutions

The DAV Maths Class 8 Solutions and DAV Class 8 Maths Chapter 10 Worksheet 2 Solutions of Parallel Lines offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 10 WS 2 Solutions

Question 1.
In the given figure l ∥ m and p ⊥ l and q ⊥ m. Show that p ∥ q. Give reasons for your answer. p ⊥1 (given)
q ⊥ m (given)
l ∥ m (given)
∴ p ∥ q
(The lines perpendicular to the parallel lines are also parallel to each other).
Hence proved. Question 2. In Fig, p ⊥ l, q ⊥ m and l ∥ m
∴ the quadrilateral ABCD may be square or a rectangle.
Reason: ∠ABC = 90° (given)
∠CDA = 180° – 90° = 90°
Hence the quadrilateral ABCD is a square or rectangle.

Question 3.
In the given figure, ABC is a triangle and AD is an altitude, show that: (i) $$\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{AD}}$$
∠PBA = 40° (Given)
But they are alternate angles.
∴ $$\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{AD}}$$

(ii) $$\overrightarrow{\mathrm{CQ}} \| \overrightarrow{\mathrm{AD}}$$
∠QCD = 90° (Given)
But they are alternate angles.

(iii) $$\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{CQ}}$$
$$\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{AD}}$$ [From (i)]
$$\overrightarrow{\mathrm{CQ}} \| \overrightarrow{\mathrm{AD}}$$ [from (ii)]
∴ $$\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{CQ}}$$
Hence Proved.

Question 4.
Draw a line segment AB of length 5 cm. At A and B, construct lines perpendicular to AB. Also, draw the perpendicular bisector of AB. Are these three lines parallel to each other? Justify your answer.
CE ⊥ AB (By construction)
AD ∥ CE …(i) [The lines perpendicular to the same line are parallel to each other.] Similarly, CE ∥ BF …(ii)
From (i) and (ii), we get
Hence proved. Question 5.
If ∠D AC = 30°, find the angles of ΔABC in the figure. 