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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?
In the context of angles, what does a linear pair consist of?
In the context of angles, what does a linear pair consist of?
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?
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?
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What is the measure of angle ∠ AOB?
What is the measure of angle ∠ AOB?
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Can you say that ∠ AOC + ∠ BOC = 180°?
Can you say that ∠ AOC + ∠ BOC = 180°?
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What is the conclusion derived from Axiom 6.1?
What is the conclusion derived from Axiom 6.1?
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'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?
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'Linear pair' refers to which type of angle relationship?
'Linear pair' refers to which type of angle relationship?
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'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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Description
This quiz explores the concept of adjacent angles and non-adjacent angles in geometry. It discusses how the sum of adjacent angles is equal to the angle formed by the two non-common arms. Understanding the positioning of non-common arms relative to a common vertex is crucial in identifying adjacent angles.
