Unit Test Solutions: Parallel and Intersecting Lines | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers  9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Directions: Questions 1–5 refer to the figure below. For each given pair of lines, identify whether they are parallel, perpendicular, or intersecting

Q1.  Lines FQ and HT are ___________ lines.  (1 Mark)

Sol: Lines FQ and HT are intersecting lines.

Q2.  Lines FQ and MW are ___________ lines. (1 Mark)

Sol: Lines FQ and MW are parallel lines.

Q3.  Lines CN and FQ are ___________ lines. (1 Mark)

Sol: Lines CN and FQ are perpendicular lines.

Q4.  Lines DZ and YG are ___________ lines. (1 Mark)

Sol: Lines DZ and YG are perpendicular lines,

Q5.  Lines CN and YG are ___________ lines. (1 Mark)

Sol:  Lines CN and YG are perpendicular lines.

Q6. Write down each pair of adjacent angles shown in the following figure (2 Mark)

Sol:

The angles that have common vertex and a common arm are known as adjacent angles
Therefore the adjacent angles in the given figure are:
∠DOC and ∠BOC
∠DOB and ∠BOA
∠COB and ∠BOA
∠AOC and ∠COD​​​​​

Q7.  In given figure, if ∠c is 120°, figure out the measurements of ∠a, ∠b, and ∠d, without drawing and measuring them? (2 Mark)

Sol: ∠d = 180° - ∠c 
∠d = 180° - 120° = 60° (linear pair).
∠c = ∠a = 120° (vertically opposite).
∠d = ∠b = 60° (vertically opposite).

Q8. Two angles form a straight line. One angle measures 102°. What is the other? (2 Mark)

Sol: Angles on a straight line add up to 180° (linear pair).
So,
180° − 102° = 78°

Q9. State which lines are parallel and why? (3 Mark)

​Sol: If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
Since ∠EQR = ∠PRQ =110° and lines FE and PR are intersected by a transversal DC such that the pair of alternate angles is equal.
So, FE || PR.

Q10.List all the linear pairs and vertically opposite angles you observe in Figure. (3 Mark)

Sol:  Linear Pairs: These are angles that are adjacent and form a straight line (add up to 180°).

• ∠a and ∠b
• ∠b and ∠c
• ∠c and ∠d
• ∠d and ∠a

Vertically Opposite Angles: These are angles that are opposite each other when two lines intersect (they are equal). 

• ∠b and ∠d (they are opposite each other at the intersection). 
• ∠a and ∠c (they are opposite each other at the intersection).

Q11.  Find the measure of angle 'a' and angle 'b'.  (3 Mark)

Sol: 

⇒ 67° + bº + 90° = 180° ( Using angles on a straight line)
⇒ bº = 180° - 67° = 23°
⇒ a° = bº ( Also, alternate angles are equal).
⇒ bº = 23°

Q12. In the given figure, l || m and t is a transversal. If ∠1 = 55°, find ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8. (5 Mark)

Sol:

Since l || m and ∠1 = 55°

So, ∠3 = ∠1 = 55° (Vertically opposite angles)

and ∠1 + ∠2 = 180° (Linear pair)

or, ∠2 = 180° – ∠1 = 180° – 55° = 125°

Also, ∠5 = ∠3 = 55° (Alternate interior angles)

Now, ∠4 + ∠5 = 180°

(Interior angles on the same side of the transversal)

or ∠4 = 180° – ∠5 = 180° – 55° = 125°

Also, ∠6 = ∠2 = 125° (Corresponding angles)

Now ∠5 = ∠7 = 55° (Vertically opposite angles)

Also, ∠6 = ∠8 = 125° (Vertically opposite angles)

Hence, ∠2 = 125°, ∠3 = 55°, ∠4 = 125°, ∠5 = 55°, ∠6 = 125°, ∠7 = 55° and ∠8 = 125°.

Q13. Find whether the lines AB and CD are parallel or not. (5 Mark)

Sol:

∠CIF + ∠FIJ = 180°  [Linear pair]

∠CIF = 180° - ∠FIJ

= 180° - 50°= 130°

So, ∠ALI = ∠CIF = 130° .

If two parallel lines are intersected by a transversal, then each pair of corresponding angles are equal.

Here, ∠ALI = ∠CIF = 130° are two corresponding angles.

Hence, AB || CD