Class 9 Mathematics Chapter 5: Parallel and Intersecting Lines – 30 CBSE MCQs with Solutions

The 2024-25 CBSE curriculum emphasises conceptual clarity over rote learning, and multiple-choice questions are the gold standard for this shift. MCQs force you to think critically: you must eliminate incorrect options, apply theorems, and justify your reasoning—not just recall formulas. In Class 9 Mathematics, the internal assessment now includes competency-based questions that mimic MCQ logic. For Chapter 5 (Parallel and Intersecting Lines), examiners test whether you can identify angle types when a transversal cuts parallel lines, apply angle sum properties, and visualise geometric configurations. MCQs also expose your blind spots instantly. If you choose 'corresponding angles are equal' for co-interior angles, you'll know immediately to review that property. Board exams allocate 20–25% weightage to MCQs in some regions, making proficiency non-negotiable. Furthermore, assertion-reason MCQs (increasingly common) demand deeper reasoning: you must justify *why* a statement is true, not just whether it is. This quiz format mirrors actual exam patterns, so practising here builds exam temperament and speed.

**Q1.** If two lines intersect, how many pairs of vertically opposite angles are formed? (A) 1 pair (B) 2 pairs (C) 3 pairs (D) 4 pairs **Answer:** (B) 2 pairs **Reason:** Two intersecting lines create four angles; opposite pairs are equal, giving 2 distinct pairs. --- **Q2.** When a transversal cuts two parallel lines, how many angles are formed in total? (A) 4 angles (B) 6 angles (C) 8 angles (D) 10 angles **Answer:** (C) 8 angles **Reason:** The transversal creates 4 angles at each intersection point; 2 lines × 4 angles = 8 total. --- **Q3.** Corresponding angles are formed when a transversal cuts two parallel lines. Which statement is true? (A) They are supplementary (B) They are equal (C) They are complementary (D) They differ by 90° **Answer:** (B) They are equal **Reason:** Corresponding angles on the same side of the transversal are always equal for parallel lines (NCERT Theorem 6.4). --- **Q4.** Two parallel lines are cut by a transversal. If one alternate interior angle is 65°, what is the other? (A) 25° (B) 65° (C) 115° (D) 155° **Answer:** (B) 65° **Reason:** Alternate interior angles are equal when formed by parallel lines and a transversal. --- **Q5.** Co-interior angles (also called consecutive interior angles) formed by parallel lines and a transversal are: (A) Equal (B) Complementary (C) Supplementary (D) Vertically opposite **Answer:** (C) Supplementary **Reason:** Co-interior angles on the same side of a transversal sum to 180° (NCERT Theorem 6.5). --- **Q6.** If line AB ∥ line CD and a transversal EF cuts them, and one corresponding angle is 72°, find the angle on the opposite side of the transversal at the same intersection. (A) 72° (B) 108° (C) 18° (D) 90° **Answer:** (B) 108° **Reason:** Corresponding angles are 72°; the adjacent angle on the transversal is supplementary, so 180° − 72° = 108°. --- **Q7.** Which pair of angles must be equal when two parallel lines are cut by a transversal? (A) Adjacent angles (B) Alternate exterior angles (C) Co-interior angles (D) All angles formed **Answer:** (B) Alternate exterior angles **Reason:** Alternate exterior angles (outside the parallel lines, on opposite sides of transversal) are equal. --- **Q8.** If two lines are parallel, then they: (A) Meet at one point (B) Do not meet at any point (C) Are perpendicular (D) Form 45° angles **Answer:** (B) Do not meet at any point **Reason:** Parallel lines maintain constant distance and never intersect (definition from NCERT). --- **Q9.** In the diagram, if AB ∥ CD and ∠AEF = 110° (where EF is the transversal), what is ∠EFD (the corresponding angle)? (A) 70° (B) 110° (C) 60° (D) 180° **Answer:** (B) 110° **Reason:** Corresponding angles formed by parallel lines and a transversal are always equal. --- **Q10.** Two co-interior angles formed by parallel lines and a transversal measure (2x) and (3x − 30)°. Find x: (A) 36° (B) 42° (C) 30° (D) 48° **Answer:** (B) 42° **Reason:** Co-interior angles are supplementary: 2x + (3x − 30) = 180 → 5x = 210 → x = 42°.

**Q11.** A transversal intersects two parallel lines. If one interior angle on one side is 120°, what is the sum of both co-interior angles? (A) 120° (B) 180° (C) 240° (D) 360° **Answer:** (B) 180° **Reason:** Co-interior angles (same side of transversal, between parallel lines) always sum to 180° by definition. --- **Q12.** Lines AB and CD are parallel. Transversal EF cuts them at points P and Q. If ∠APE = 85°, find ∠PQD: (A) 85° (B) 95° (C) 105° (D) 180° − 85° = 95° **Answer:** (D) 105° (if exterior angle) **Reason:** ∠APE and ∠PQD are co-exterior angles; if interior positions differ, use supplementary property. --- **Q13.** In triangle ABC, if a line parallel to BC is drawn through point D on AB and E on AC, then by the Basic Proportionality Theorem (Thales' Theorem), which is true? (A) AD/DB = AE/EC (B) AD/AB = AE/AC (C) AB/AD = AC/AE (D) DB/AB = EC/AC **Answer:** (A) AD/DB = AE/EC **Reason:** When DE ∥ BC, the sides are divided proportionally: AD/DB = AE/EC (NCERT Theorem 6.2). --- **Q14.** A transversal cuts two lines. The alternate interior angles are equal. What can you conclude? (A) The lines are perpendicular (B) The lines are parallel (C) The lines are skew (D) The lines are concurrent **Answer:** (B) The lines are parallel **Reason:** Equal alternate interior angles is a sufficient condition to prove lines are parallel (NCERT Converse of Theorem 6.4). --- **Q15.** Two parallel lines are cut by two different transversals. How many points of intersection are there (excluding the parallel lines)? (A) 0 points (B) 1 point (C) 2 points (D) 4 points **Answer:** (B) 1 point **Reason:** Two transversals cutting two parallel lines intersect each other at exactly one point (unless they are parallel). --- **Q16.** If ∠1 and ∠2 are corresponding angles formed by parallel lines and a transversal, and ∠1 = 4x + 10 and ∠2 = 6x − 30, find the value of x: (A) 10 (B) 15 (C) 20 (D) 25 **Answer:** (C) 20 **Reason:** Corresponding angles are equal: 4x + 10 = 6x − 30 → 40 = 2x → x = 20°. --- **Q17.** A transversal intersects two parallel lines. If one exterior angle is 65°, which interior angle on the opposite side is: (A) 65° (alternate exterior) (B) 115° (supplementary to interior) (C) 180° − 65° = 115° (co-exterior supplementary) (D) 45° **Answer:** (C) 115° **Reason:** Exterior 65° and its co-interior angle (same side, interior) sum to 180°, so interior = 115°. --- **Q18.** In a quadrilateral ABCD, if AB ∥ CD, which property holds? (A) ∠A + ∠B = 180° (B) ∠A + ∠D = 180° (C) ∠B + ∠C = 180° (D) All angles are equal **Answer:** (B) ∠A + ∠D = 180° **Reason:** In a trapezoid (one pair of parallel sides), co-interior angles are supplementary: ∠A + ∠D = 180°. --- **Q19.** A line is drawn parallel to the base BC of triangle ABC, intersecting AB at D and AC at E. If AD = 3 cm, DB = 6 cm, and AE = 4 cm, find EC: (A) 6 cm (B) 8 cm (C) 12 cm (D) 2 cm **Answer:** (B) 8 cm **Reason:** By Basic Proportionality Theorem: AD/DB = AE/EC → 3/6 = 4/EC → EC = 8 cm. --- **Q20.** If two lines are cut by a transversal and the sum of co-interior angles is 180°, then: (A) The lines are perpendicular (B) The lines are parallel (C) The lines intersect at 45° (D) The lines are skew **Answer:** (B) The lines are parallel **Reason:** Co-interior angles summing to 180° is both a necessary and sufficient condition for parallel lines (NCERT Converse of Theorem 6.5).

**Q21.** **Assertion (A):** If a transversal is perpendicular to one of two parallel lines, it is perpendicular to the other. **Reason (R):** Corresponding angles formed by a transversal and parallel lines are equal. (A) Both A and R are true; R is the correct explanation of A (B) Both A and R are true; R is not the correct explanation of A (C) A is true, but R is false (D) A is false, but R is true **Answer:** (A) Both A and R are true; R is the correct explanation of A **Reason:** If transversal ⊥ first line, corresponding angle = 90°; by equality, transversal ⊥ second line. R explains A. --- **Q22.** **Assertion (A):** In a triangle, a line drawn parallel to one side divides the other two sides proportionally. **Reason (R):** This is a consequence of the Basic Proportionality Theorem (Thales' Theorem). (A) Both A and R are true; R explains A (B) Both A and R are true; R doesn't explain A (C) A is true, but R is false (D) Both A and R are false **Answer:** (A) Both A and R are true; R explains A **Reason:** NCERT Theorem 6.2 directly states this; R provides the theoretical foundation for A. --- **Q23.** **Assertion (A):** If ∠1 and ∠2 are alternate interior angles formed by a transversal cutting two lines, and ∠1 = ∠2, then the lines must be parallel. **Reason (R):** Alternate interior angles are always equal for any two lines. (A) A is true, but R is false (B) Both A and R are true; R explains A (C) A is true; R is irrelevant (D) Both A and R are false **Answer:** (A) A is true, but R is false **Reason:** A is the converse of Theorem 6.4 (true by NCERT); R is false because alternate angles are equal *only for parallel lines*. --- **Q24.** **Assertion (A):** In quadrilateral PQRS, if PQ ∥ SR, then ∠P + ∠S = 180° and ∠Q + ∠R = 180°. **Reason (R):** Co-interior angles on the same side of a transversal cutting parallel lines are supplementary. (A) Both A and R are true; R explains A (B) A is true, but R is incomplete (C) Both A and R are true; R partially explains A (D) A is false; R is true **Answer:** (C) Both A and R are true; R partially explains A **Reason:** A is true (trapezoid property); R is true but only explains half of A (need transversals PS and QR). --- **Q25.** **Assertion (A):** If a line intersects two parallel lines, it creates eight angles, and exactly four of them are acute and four are obtuse (unless the transversal is perpendicular). **Reason (R):** Corresponding angles are equal, and adjacent angles on a line are supplementary. (A) Both A and R are true; R explains A (B) A is true, but R is incomplete (C) Both A and R are true, but R doesn't fully explain A (D) A is false; R is true **Answer:** (A) Both A and R are true; R explains A **Reason:** Four angles will be ≤ 90° and four > 90° (or all 90° if perpendicular); R provides the reasoning via angle properties. --- **Q26.** **Assertion (A):** In triangle XYZ, if a line parallel to YZ passes through a point P on XY (with XP = 2 cm, PY = 3 cm) and intersects XZ at Q, then XQ:QZ = 2:3. **Reason (R):** The converse of the Basic Proportionality Theorem states that a line dividing two sides proportionally is parallel to the third side. (A) A is true; R is about converse (not direct proof) (B) Both A and R are true; R is not the reason for A (C) A is true; R addresses the converse, not the forward theorem (D) Both A and R are false **Answer:** (B) Both A and R are true; R is not the reason for A **Reason:** A follows from the forward Basic Proportionality Theorem; R is about the converse direction. --- **Q27.** **Assertion (A):** If two lines are cut by a transversal such that one pair of alternate interior angles is equal, then all pairs of corresponding angles are also equal. **Reason (R):** If alternate interior angles are equal, the lines are parallel; and for parallel lines, corresponding angles are equal. (A) Both A and R are true; R explains A (B) A is true, but R is unnecessary (C) A is false; R is true (D) Both A and R are false **Answer:** (A) Both A and R are true; R explains A **Reason:** One pair of equal alternate interior angles ⟹ parallel lines ⟹ all corresponding angles equal (chain of theorems). --- **Q28.** **Assertion (A):** Vertically opposite angles formed by two intersecting lines are always equal, regardless of the angle of intersection. **Reason (R):** Vertically opposite angles are supplementary to the same adjacent angle. (A) Both A and R are true; R explains A (B) A is true; R is an alternative proof (C) A is true, but R is incorrect reasoning (D) A is false **Answer:** (B) A is true; R is an alternative proof **Reason:** A is always true (fundamental property); R is a valid proof: ∠1 + ∠2 = 180° and ∠2 + ∠3 = 180° ⟹ ∠1 = ∠3. --- **Q29.** **Assertion (A):** When constructing a line parallel to a given line using a compass and straightedge, we can use the property that corresponding angles are equal. **Reason (R):** Construction of parallel lines relies on transferring equal angles via arc-marking. (A) Both A and R are true; R explains A (B) Both A and R are true; R doesn't fully explain A (C) A is true, but R oversimplifies (D) Both A and R are false **Answer:** (A) Both A and R are true; R explains A **Reason:** NCERT Construction 6.1 uses corresponding angles: mark equal angles, then corresponding angles guarantee parallel lines. --- **Q30.** **Assertion (A):** In a trapezium ABCD with AB ∥ CD, if the diagonals AC and BD intersect at O, then triangles AOB and COD are similar. **Reason (R):** Corresponding angles formed by parallel lines AB and CD cut by transversals AC and BD are equal. (A) Both A and R are true; R explains A (B) A is true, but R is incomplete (C) Both A and R are true; R partially explains A (D) A is false; R is true **Answer:** (C) Both A and R are true; R partially explains A **Reason:** A is true (AA similarity); R is true and helps, but similarity also requires ∠AOB = ∠COD (vertically opposite), so R is partial.

MCQs in parallel lines often use psychological traps. Here are the most dangerous ones: **Trap 1: Confusing Alternate Interior with Co-Interior Angles** Students often think "alternate" means "on opposite sides" and jump to co-interior. Remember: Alternate interior angles are *equal* (on opposite sides of transversal, between parallel lines), while co-interior angles are *supplementary* (on the same side, sum to 180°). If the question says "angles on the same side," it's co-interior—they add to 180°, not equal. **Trap 2: Forgetting the "Parallel Lines" Condition** Many options state angle properties *without confirming the lines are parallel*. For example: "If ∠1 = ∠2, then the lines are parallel" is true. But "If ∠1 = ∠2, then they are corresponding angles" might be false if the lines aren't parallel. Always check: *are the lines actually parallel?* If not, angle equality doesn't follow the standard properties. **Trap 3: Misidentifying Angle Positions** Diagrams can be rotated or redrawn, causing confusion about which angles are corresponding, alternate, or co-interior. Draw the transversal clearly: angles on opposite sides of the transversal, between the parallel lines = alternate interior. Same side, between lines = co-interior. Same relative position on either line = corresponding. Count the sides carefully before choosing. **Trap 4: Assuming Perpendicularity Without Evidence** If one angle is 90°, students assume all angles are 90°. But unless stated, a transversal *isn't* perpendicular. If ∠1 = 90°, then ∠2 (corresponding) = 90°, but ∠3 (adjacent) = 90° only if the transversal is perpendicular to the line. **Trap 5: Mixing Up Supplementary and Complementary** Supplementary = 180° sum; Complementary = 90° sum. In parallel lines + transversal, co-interior angles are supplementary (180°). A wrong option might say "complementary (90°)"—this is false. **Trap 6: Ignoring the "Converse" in Reasoning MCQs** Assertion-Reason MCQs often test converses. For example: "If lines are parallel, then alternate interior angles are equal" (true). The converse: "If alternate interior angles are equal, then lines are parallel" (also true—it's a condition for parallelism). But some converses are false. Always check if R is the *correct explanation* of A, or just a true but separate fact. **Trap 7: Vertical Angles vs. Vertically Opposite** "Vertical angles" sometimes confuses students with angles at the top/bottom of a diagram. They're the same as vertically opposite angles (formed by two intersecting lines, always equal). Don't mix this up with angles formed by a vertical line. **Trap 8: Miscounting Total Angles** If a transversal cuts two parallel lines, students sometimes count 4 angles instead of 8, or forget that adjacent supplementary angles are different from the 8 angles formed. Always visualise: each intersection point has 4 angles, 2 intersection points = 8 total. **Safety Strategy:** For every MCQ, restate the given condition aloud: "Parallel lines? Yes. Transversal cutting them? Yes. Which angles am I comparing?" This narration prevents misreading trap options.

Board exams and competitive tests allocate limited time for MCQs. Here's a proven strategy for Class 9 Chapter 5: **Phase 1: Quick Scan (1 minute per question)** Read the question, identify whether it's about angle types, angle values, or geometric proof. If it involves corresponding angles, your brain should immediately recall "they're equal" (for parallel lines). Don't solve yet—just classify: - **Type A:** Identify angle category (corresponding, alternate, co-interior) → Instant recall (20 seconds) - **Type B:** Calculate angle value given one angle and parallel/non-parallel lines → Algebra (1–2 minutes) - **Type C:** Assertion-Reason or geometric proof → Deep reasoning (2–3 minutes) **Phase 2: Answer Easy Questions First (60 seconds per question)** Do all Type A questions in the first pass. Questions 1–10 from our quiz are easy—angle identification, basic properties. These are free marks. Skip them if you doubt; come back later. **Phase 3: Moderate-Difficulty Calculations (90 seconds per question)** Now tackle Type B (Questions 11–20). Set up the equation immediately: - Co-interior angles: x + y = 180° - Corresponding angles: x = y - Alternate interior: x = y Substitute given values, solve, check if answer is in the options. If not, re-read the question—you likely misidentified the angle type. **Phase 4: Assertion-Reason Last (2–3 minutes per question)** Type C (Questions 21–30) require reading two statements carefully. Strategy: 1. Judge A (true or false?) based on NCERT theorems. 2. Judge R (true or false?) independently. 3. Does R explain A? (Not just "both true"—but does R provide the reason?) If time is tight, skip a tough assertion-reason and return if time permits. **Time Allocation (for a 30-question MCQ in 45 minutes):** - First scan: 30 questions × 1 minute = 30 minutes - Solve easy (Q1–10): 10 minutes - Solve medium (Q11–20): 15 minutes - Solve hard/assertion-reason (Q21–30): 20 minutes - Review and corrections: 10 minutes If you have 60 minutes, you can solve more carefully; if 30 minutes, focus on speed and accuracy trade-off. **Red Flags That Signal a Trap:** - Option says "always" or "never"—extreme claims are often false. - An option repeats words from the question verbatim—check if it's a distractor. - Two options are almost identical—compare the single difference carefully. - An option seems "too easy" for a medium question—re-read the question stem. **Checksum Before Submitting:** - Do all angle sums make sense (180°, 360°)? - Are parallel line properties applied *only* when lines are confirmed parallel? - Did you convert all angles to the same unit (degrees)? - For proportionality questions, did you cross-multiply correctly? With consistent practice of this strategy on our 30-question quiz, you'll solve exam MCQs in 1–1.5 minutes per question, building both accuracy and speed.

Practising MCQs isn't passive reading—it's active problem-solving. Here's how to extract full value: **Step 1: Attempt All 30 MCQs Under Timed Conditions (45 minutes)** Set a timer and solve without referring to textbooks or answers. Treat it like an exam. This reveals your actual level and gaps. Mark questions you're unsure about with a star. **Step 2: Check Answers and Analyse Mistakes** For each wrong answer, ask: "Why did I choose the wrong option?" Was it a calculation error, misidentification of angle type, or misreading the question? Write down the reason. This pattern recognition is crucial. **Step 3: Review the 1-Line Reason for Each Question** Our explanations are concise and theorem-based. Cross-reference with NCERT Chapter 6: you'll find Theorems 6.1–6.5 and Constructions 6.1–6.3 mentioned. Strengthen your understanding by reading the NCERT text once more for the relevant theorem. **Step 4: Reattempt Only the Questions You Got Wrong** Wait 24 hours, then retake only the starred questions. If you get them right the second time, you've solidified that concept. If you repeat the same mistake, you need deeper study—revisit the NCERT example or construct a diagram. **Step 5: Create a Personal Weak-Spot List** If many wrong answers involve co-interior angles, prioritise that concept. Write out the property: "Co-interior angles sum to 180°." Memorise it. Draw 3–4 examples yourself. Teach it to a friend aloud. Repetition + varied output = retention. **Step 6: Attempt the Quiz Again After 1 Week** Re-solve all 30 MCQs after a week of studying the weak spots. Your score should improve significantly. Aim for 90%+ (27/30). If you hit that, you're ready for the board exam on this chapter. **Bonus: Print and Share** If you're part of a study group, print this quiz and solve it together. Discuss why each answer is correct—peer explanation deepens understanding faster than solo revision. At cbsetutor.ai, our AI tutors personalise this feedback, identifying your specific misconceptions and adapting the difficulty in real time.