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.
DAV Class 8 Maths Chapter 10 Worksheet 2 Solutions 1
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.
What can you say about the quadrilateral ABCD given in figure. Is it a rectangle? Justify your answer.
DAV Class 8 Maths Chapter 10 Worksheet 2 Solutions 1
Answer:
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:
DAV Class 8 Maths Chapter 10 Worksheet 2 Solutions 2
(i) \(\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{AD}}\)
Answer:
∠PBA = 40° (Given)
∠BAD = 40° (Given)
∴ ∠PBA = ∠BAD
But they are alternate angles.
∴ \(\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{AD}}\)

(ii) \(\overrightarrow{\mathrm{CQ}} \| \overrightarrow{\mathrm{AD}}\)
Answer:
∠ADC = 90° (Given)
∠QCD = 90° (Given)
∴ ∠ADC ∥∠QCD
But they are alternate angles.

(iii) \(\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{CQ}}\)
Answer:
\(\overrightarrow{\mathrm{BP}} \| \overrightarrow{\mathrm{AD}}\) [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.
Answer:
AD ⊥ AB (Given)
CE ⊥ AB (By construction)
AD ∥ CE …(i) [The lines perpendicular to the same line are parallel to each other.]
DAV Class 8 Maths Chapter 10 Worksheet 2 Solutions 3
Similarly, CE ∥ BF …(ii)
From (i) and (ii), we get
AD ∥ CE ∥ BF
Hence proved.

Question 5.
If ∠D AC = 30°, find the angles of ΔABC in the figure.
DAV Class 8 Maths Chapter 10 Worksheet 2 Solutions 2
Answer:
∠DAC = 30° (given)
∴ ∠BAC = ∠DAC + ∠BAD
= 30° + 40° = 70°
∠PBD = 90° (given)
∴ ∠ABC = ∠PBD – 40°
= 90° – 40° = 50°
∠ACB = 180° – (70° + 50°)
= 180° – 120° = 60°.