Q1: What is the measure of an angle formed when two rays meet at a common point called a vertex? (a) It depends on the turn between the two rays (b) It is always 90 degrees (c) It is always 180 degrees (d) It is measured in metres
Solution:
Ans: (a) Explanation: An angle is formed by the turn between two rays around their common point or vertex, and its measure depends on this turn.
Q2: Which term describes a collection of points with two fixed endpoints? (a) Ray (b) Line segment (c) Line (d) Point
Solution:
Ans: (b) Explanation: A line segment is defined as a collection of points with two fixed endpoints, and its length is fixed, unlike a line or ray.
Q3: When a transversal intersects two parallel lines, what is the relationship between alternate interior angles? (a) They are supplementary (b) They form a linear pair (c) They are equal (d) They total 90 degrees
Solution:
Ans: (c) Explanation: When a transversal cuts two parallel lines, each pair of alternate interior angles is equal, which is a fundamental property of parallel lines.
Q4: What is the sum of two supplementary angles? (a) 90° (b) 45° (c) 270° (d) 180°
Solution:
Ans: (d) Explanation: Two angles are supplementary when the sum of their measures equals 180°, and each angle is called the supplement of the other.
Q5: If two lines lying in the same plane do not intersect when produced on either side, what are they called? (a) Perpendicular lines (b) Intersecting lines (c) Transversal lines (d) Parallel lines
Solution:
Ans: (d) Explanation: Lines that lie in the same plane and do not intersect when extended on either side are defined as parallel lines.
Fill in the Blanks
Q1: An exact location that has no size, only position, is called a _____.
Solution:
Ans: point
Q2: The point at which two rays meet to form an angle is called the _____ of the angle.
Solution:
Ans: vertex
Q3: When the sum of the measures of two angles is 90°, the angles are called _____ angles.
Solution:
Ans: complementary
Q4: A line that intersects two or more lines in a plane at distinct points is called a _____ line.
Solution:
Ans: transversal
Q5: The length of a ray is _____.
Solution:
Ans: infinite
True or False
Q1: A line segment has infinite length.
Solution:
Ans: False Explanation: A line segment has two fixed endpoints, and therefore its length is fixed, not infinite like a line or ray.
Q2: When two angles are complementary, each angle is said to be the complement of the other.
Solution:
Ans: True Explanation: Whenever two angles are complementary, each angle is indeed said to be the complement of the other angle by definition.
Q3: A ray has two fixed endpoints.
Solution:
Ans: False Explanation: A ray has only one fixed point and extends endlessly from the other end, making it different from a line segment.
Q4: When a transversal intersects two parallel lines, each pair of corresponding angles is equal.
Solution:
Ans: True Explanation: When a transversal cuts two parallel lines, each pair of corresponding angles is equal, which is a property of parallel lines.
Q5: Two lines are intersecting when they cross each other at multiple points.
Solution:
Ans: False Explanation: Two lines are intersecting when they cross each other at one point only, which is called the point of intersection.
Match the Following
Column A
Column B
1. A part of a line with one fixed point extending endlessly from the other end
A. Supplementary angles
2. Two angles whose sum equals 180°
B. Point
3. The point where two rays meet to form an angle
C. Transversal line
4. An exact location with no size, only position
D. Ray
5. A line intersecting two or more lines at distinct points
E. Vertex
Solution:
Ans:
1 - D: A ray is defined as a part of a line with one fixed point extending endlessly from the other end.
2 - A: Supplementary angles are two angles whose sum of measures equals 180°, with each being the supplement of the other.
3 - E: The vertex is the point at which two rays meet to form an angle, serving as the common initial point.
4 - B: A point is an exact location that has no size, including no length, width, or depth, only position.
5 - C: A transversal line is one that intersects two or more lines in a plane at distinct points, creating various angle relationships.
Short Answer Questions
Q1: What are complementary angles? Explain with an example.
Solution:
Ans: Complementary angles are two angles whose sum equals 90°. Each angle is called the complement of the other. For example, if ∠PQS measures 50° and ∠SQR measures 40°, then their sum is 90°. Therefore, ∠PQS and ∠SQR are complementary angles and are complements of each other.
Q2: Distinguish between a line, a ray, and a line segment based on their endpoints and length.
Solution:
Ans: A line segment has two fixed endpoints and a fixed length. A ray has one fixed point and extends endlessly from the other end, giving it infinite length. A line is a collection of points extending endlessly in both directions along a straight path, also having infinite length but no fixed endpoints.
Q3: What is a transversal line and what angles does it create?
Solution:
Ans: A transversal line intersects two or more lines in a plane at distinct points. When it intersects two lines, it creates eight angles at the two points of intersection. These angles include pairs of corresponding angles, alternate interior angles, alternate exterior angles, and interior angles on the same side of the transversal.
Q4: How can you test if two lines are parallel using corresponding angles?
Solution:
Ans: When a transversal intersects two lines, if any pair of corresponding angles are equal, then the lines are parallel. For example, if angles formed at corresponding positions on both lines are equal, such as ∠1 = ∠5 or ∠3 = ∠7, this confirms that the two lines are parallel to each other.
Q5: What relationship exists between interior angles on the same side of a transversal when two lines are parallel?
Solution:
Ans: When a transversal intersects two parallel lines, each pair of interior angles on the same side of the transversal is supplementary, meaning their sum equals 180°. For instance, ∠3 + ∠6 = 180° and ∠4 + ∠5 = 180°. This property helps in identifying whether lines are parallel or not.
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