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Questions and Answers
What is the equal length between two parallel lines called?
What is the equal length between two parallel lines called?
- Diagonal length
- Perpendicular distance (correct)
- Parallel offset
- Bisector distance
In the context of angles, what does a linear pair consist of?
In the context of angles, what does a linear pair consist of?
- Two adjacent angles whose sum is 180° (correct)
- Two opposite angles that add up to 90°
- Two opposite angles that add up to 180°
- Two adjacent angles whose sum is 90°
According to Axiom 6.1, what is the sum of two adjacent angles when a ray stands on a line?
According to Axiom 6.1, what is the sum of two adjacent angles when a ray stands on a line?
- 120°
- 180° (correct)
- 90°
- 270°
What are the names of the angles formed at point O in the figure?
What are the names of the angles formed at point O in the figure?
What is the measure of angle ∠AOB?
What is the measure of angle ∠AOB?
Can you say that ∠AOC + ∠BOC = 180°?
Can you say that ∠AOC + ∠BOC = 180°?
What is the conclusion derived from Axiom 6.1?
What is the conclusion derived from Axiom 6.1?
'If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.' This statement refers to which geometric concept?
'If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.' This statement refers to which geometric concept?
'Linear pair' refers to which type of angle relationship?
'Linear pair' refers to which type of angle relationship?
'Adjacent angles' are defined as angles that:
'Adjacent angles' are defined as angles that:
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Study Notes
Angles and Lines
- Ray BD is the common arm and point B is the common vertex of two angles.
- Ray BA and ray BC are non-common arms of two angles.
- The sum of two adjacent angles is equal to the angle formed by the two non-common arms.
Adjacent Angles
- ∠ABC and ∠ABD are not adjacent angles because their non-common arms BD and BC lie on the same side of the common arm BA.
- When two angles are adjacent, their sum is equal to the angle formed by the two non-common arms.
Linear Pair of Angles
- When the non-common arms of two angles form a line, the angles are called a linear pair of angles.
- Example: ∠ABD and ∠DBC are a linear pair of angles in Fig. 6.3.
Vertically Opposite Angles
- When two lines intersect, they form vertically opposite angles.
- Example: ∠AOD and ∠BOC are vertically opposite angles in Fig. 6.4.
Intersecting and Non-Intersecting Lines
- Two lines can be drawn in two different ways: intersecting or non-intersecting (parallel).
- Example: Fig. 6.5 shows two different ways of drawing lines PQ and RS.
Properties of Lines
- A line extends indefinitely in both directions.
- Lines can be intersecting or parallel.
Example Problems
- If two lines are parallel, corresponding angles are equal.
- Example: In Fig. 6.19, if PQ || RS, ∠MXQ = 135° and ∠MYR = 40°, then ∠XMY = 85°.
- If a transversal intersects two lines and the bisectors of a pair of corresponding angles are parallel, then the two lines are parallel.
- Example: In Fig. 6.21, if ray BE is the bisector of ∠ABQ and ray CG is the bisector of ∠BCS, and BE || CG, then PQ || RS.
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