Chapter-5 Parallel and Intersecting Lines — Online MCQ Test
MATHS · Grade 7 · CBSE(NCERT)
Practice Chapter-5 Parallel and Intersecting Lines with a free chapter-wise online MCQ test.
This chapter covers: parallel lines - intersecting lines - perpendicular - transversal - angle relationships.
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Chapter-5 Parallel and Intersecting Lines — Important Questions & Answers
Two lines that do not intersect at any point and are always at the same distance apart are called:
- A. Perpendicular lines
- B. Parallel lines
- C. Intersecting lines
- D. Coincident lines
Answer: B. Parallel lines
Parallel lines are lines that never meet and maintain a constant distance. This is the definition of parallel lines in geometry.
Parallel lines are lines that never meet and maintain a constant distance. This is the definition of parallel lines in geometry.
Which symbol is used to denote that two lines are parallel?
- A. ⊥
- B. ||
- C. ∠
- D. ≈
Answer: B. ||
The symbol '||' is the standard mathematical notation used to indicate that two lines are parallel to each other.
The symbol '||' is the standard mathematical notation used to indicate that two lines are parallel to each other.
Two lines that meet at a point and form a 90° angle are called:
- A. Parallel lines
- B. Oblique lines
- C. Perpendicular lines
- D. Skew lines
Answer: C. Perpendicular lines
Perpendicular lines are lines that intersect at right angles (90°). The symbol ⊥ is used to denote perpendicular lines.
Perpendicular lines are lines that intersect at right angles (90°). The symbol ⊥ is used to denote perpendicular lines.
A line that intersects two or more lines at different points is called a:
- A. Parallel line
- B. Transversal
- C. Perpendicular line
- D. Concurrent line
Answer: B. Transversal
A transversal is a line that cuts across two or more other lines at different points, creating various angle relationships.
A transversal is a line that cuts across two or more other lines at different points, creating various angle relationships.
If line AB || line CD and a transversal EF intersects both, then which angles are equal?
- A. Only corresponding angles
- B. Only alternate interior angles
- C. Both corresponding and alternate interior angles
- D. Only co-interior angles
Answer: C. Both corresponding and alternate interior angles
When a transversal intersects two parallel lines, both corresponding angles and alternate interior angles are equal properties of parallel lines.
When a transversal intersects two parallel lines, both corresponding angles and alternate interior angles are equal properties of parallel lines.
In the figure, if lines l and m are parallel and t is a transversal, and one angle is 65°, what is the measure of its corresponding angle?
- A. 65°
- B. 115°
- C. 90°
- D. 125°
Answer: A. 65°
Corresponding angles formed when a transversal intersects parallel lines are equal in measure, so if one is 65°, its corresponding angle is also 65°.
Corresponding angles formed when a transversal intersects parallel lines are equal in measure, so if one is 65°, its corresponding angle is also 65°.
If angle A and angle B are vertically opposite angles, and angle A = 3x + 20, angle B = 2x + 40, find the value of x:
- A. 10
- B. 20
- C. 30
- D. 15
Answer: B. 20
Vertically opposite angles are equal, so 3x + 20 = 2x + 40. Solving: x = 20.
Vertically opposite angles are equal, so 3x + 20 = 2x + 40. Solving: x = 20.
In the given figure, lines AB and CD are parallel, EF is a transversal. If ∠AEF = 50°, find ∠EFC (assuming F is on line CD):
- A. 50°
- B. 130°
- C. 90°
- D. 100°
Answer: B. 130°
∠AEF and ∠EFC are co-interior angles (same-side interior angles), which are supplementary when lines are parallel. So ∠EFC = 180° - 50° = 130°.
∠AEF and ∠EFC are co-interior angles (same-side interior angles), which are supplementary when lines are parallel. So ∠EFC = 180° - 50° = 130°.
Two parallel lines are intersected by a transversal. One of the eight angles formed is 35°. How many of the remaining seven angles measure 145°?
- A. 2 angles
- B. 3 angles
- C. 4 angles
- D. 5 angles
Answer: C. 4 angles
When a transversal intersects two parallel lines, 4 angles of 35° and 4 angles of 145° are formed (supplementary pairs). Therefore, 4 angles measure 145°.
When a transversal intersects two parallel lines, 4 angles of 35° and 4 angles of 145° are formed (supplementary pairs). Therefore, 4 angles measure 145°.
Line l is parallel to line m. Transversal t cuts l at A and m at B. If the angle on the right side of t and above l is (5x - 5)° and the angle on the left side of t and below m is (3x + 15)°, these are co-interior angles. Find x and explain why this relationship holds:
- A. x = 17.5, co-interior angles are supplementary
- B. x = 10, co-interior angles are equal
- C. x = 20, co-interior angles are complementary
- D. x = 15, co-interior angles are equal
Answer: A. x = 17.5, co-interior angles are supplementary
Co-interior angles are supplementary: (5x - 5) + (3x + 15) = 180. Solving: 8x + 10 = 180, so x = 17.5. These angles add to 180° because they are on the same side of the transversal.
Co-interior angles are supplementary: (5x - 5) + (3x + 15) = 180. Solving: 8x + 10 = 180, so x = 17.5. These angles add to 180° because they are on the same side of the transversal.