RS Aggarwal Solutions for Class 6 Chapter 15 Polygons

Question 1. Identify parallel line segments:
(i) [Triangle with line DE parallel to BC]
(ii) [Rectangle ABCD with DC and AB marked]
(iii) [Parallelogram ABCD]
(iv) [Hexagon PQRSTU]
(v) [Two triangles forming a star shape]
(vi) [Two overlapping triangles]
Answer:
(i) BC || DE
(ii) AB || DC, AD || BC
(iii) AB || DC, AD || BC
(iv) PQ || TS, UT || QR, UP || SR
(v) AB || DC || EF, AD || BC and DE || CF
(vi) BC || E, AB || DF and AC || DE
In simple words: Look at each shape and find which line segments never meet, no matter how far you stretch them. Those are the parallel segments. Mark them using the symbol ||.

Exam Tip: Always check if line segments are on opposite sides and maintain constant distance to identify parallelism correctly.

Question 2. Name the pairs of all possible parallel edges of the pencil box whose figure is shown in the figure.
Answer:
(i) AH || DG || CF || BE
(ii) AB || DC || GF || HE
(iii) AD || HG || EF || BC
In simple words: A pencil box (cuboid) has twelve edges. Find groups of edges that run side by side and never meet. Each group contains four parallel edges.

Exam Tip: In a cuboid, parallel edges come in groups of four - think of the top and bottom faces, plus the vertical edges connecting them.

Question 3. In the figure, do the segments AB and CD intersect? Are they parallel? Give reasons.
Answer: In the given position, segments AB and CD do not intersect, though they could if extended to meet at a point. They are not parallel because the gap between them changes along their length, not remaining constant.
In simple words: Two lines that meet when extended are not parallel. Parallel lines always stay the same distance apart.

Exam Tip: Remember that true parallel lines must maintain equal distance everywhere - if the distance changes, they are not parallel.

Question 4. State which of the following are true or false:
(i) If two lines in the same plane do not intersect, then they must be parallel
(ii) Distance between two parallel lines is not same everywhere
(iii) If m perpendicular to l and n perpendicular to l and m ≠ n, then m parallel to n
(iv) Two non - intersecting co - planar rays are parallel
(v) If Ray AB parallel to m, then line segment AB parallel to m
(vi) If Ray AB parallel to m, then line segment AB parallel to m
(vii) No two parallel segments intersect each other
(viii) Every pair of lines is a pair of co-planar lines
(ix) Two lines perpendicular to the same line are parallel
(x) A line perpendicular to one of two parallel lines is perpendicular to each other
Answer:
(i) True
(ii) False
(iii) True
(iv) False
(v) True
(vi) True
(vii) True
(viii) False
(ix) True
(x) True
In simple words: When two lines don't cross in the same flat plane, they are parallel. Parallel lines keep the same distance apart everywhere. Two lines both standing upright on the same floor line will be parallel to each other.

Exam Tip: For true-false questions on parallel lines, test each statement by drawing or imagining counterexamples - this quickly reveals false statements.

Question 5. (i) Alternate corresponding angles
Answer: Alternate interior angles are angle BGH and angle CHG, as well as angle AGH and angle CHF. Alternate exterior angles are angle AGE and angle DHF, plus angle EGB and angle CHF. Corresponding angles include angle EGB and angle GHD, angle EGA and angle GHC, angle BGH and angle DHF, and angle AGF and angle CHF.
In simple words: When a line crosses two other lines, it creates eight angles. Alternate angles sit on opposite sides of the crossing line and between the two lines. Corresponding angles sit on the same side but one is inside and one is outside the two lines.

Exam Tip: Draw and label the eight angles formed when a transversal crosses two lines - this visual approach helps you spot alternate and corresponding angle pairs instantly.

Question 5. (ii) Angles alternate to ∠d and ∠g and angles corresponding to angles ∠f and ∠h in the figure
Answer: The alternate angle to ∠d is ∠e, and the alternate angles to ∠g is ∠b. The corresponding angles to ∠f is ∠c, and ∠h is ∠a.
In simple words: When you identify one angle at the first intersection point, its alternate angle sits opposite to it at the second intersection. Its corresponding angle sits in the matching position at the other intersection point.

Exam Tip: Use the Z-pattern for alternate angles and the F-pattern for corresponding angles to spot them quickly in transversal diagrams.

Question 5. (iii) Angles alternative to ∠PQR, angle corresponding to ∠RQF and angle alternative to ∠PQE in the figure
Answer: In the given figure, line 'l' is a transversal to lines 'm' and 'n'. Therefore, the alternate angle of ∠PQR is ∠QRA. The corresponding angle ∠RQF and ∠BRA. The alternate angle of ∠PQE is ∠BRA.
In simple words: A transversal cuts through two lines making multiple angles. Find the alternate angles by looking across the transversal and between the two lines. Find corresponding angles by staying on the same side of the transversal.

Exam Tip: Always identify which lines are parallel and which is the transversal first - this makes finding alternate and corresponding angles much clearer.

Question 6. Match column A and column B.
(i) Vertically opposite angles - a. ∠PAB and ∠ABS
(ii) Alternate angles - b - ∠PAB and ∠RBY
(iii) Corresponding angles - c. ∠PAB and ∠XAQ
Answer:
(i) Vertically opposite angles - c. ∠PAB and ∠XAQ
(ii) Alternate angles - a. ∠PAB and ∠ABS
(iii) Corresponding angles - b - ∠PAB and ∠RBY
In simple words: Vertically opposite angles sit across from each other when two lines cross. Alternate angles are on opposite sides of a transversal cutting two lines. Corresponding angles are on the same side, in matching positions.

Exam Tip: Draw two intersecting lines and a transversal cutting two parallel lines - label all angles and practice matching angle pairs until the patterns become automatic.