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Math Chapter 8 : Topic 1
Angles Between Lines
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The angle between two intersecting lines depends on:
Reasoning: Angle is determined using slopes of lines $\Longrightarrow$ $tan\ \theta =$ $\frac{m_{2}\ - \ m_{1}}{1\ + \ m_{1\ }m_{2}}$
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If two lines are parallel, the angle between them is:
Reasoning: Parallel lines do not intersect.
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If two lines are perpendicular, the angle between them is:
Reasoning: Perpendicular lines form right angle.
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Angle between two lines is always:
Reasoning: We take the smaller angle.
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If slopes are equal, angle between lines is:
Reasoning: Lines are parallel.
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If $\ m_{1}{\ m}_{2} = - \ 1$, then angle between lines is:
Reasoning: Condition of perpendicularity.
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Which formula is used for angle between two lines?
Reasoning: Uses tangent of angle $\Longrightarrow$ $tan\ \theta =$ $\frac{m_{2}\ - \ m_{1}}{1\ + \ m_{1}{\ m}_{2}}$
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If slopes are $1$ and $1$, angle between lines is:
Reasoning: Same slope $\Longrightarrow$ parallel lines
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If slopes are $2$ and $- \ 2$, lines are:
Reasoning: Product not equal to $- \ 1$.
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Angle between identical lines is:
Reasoning: Same line $\Longrightarrow$ no angle
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If $m_{1} = 0$ and $m_{2} = 1$, angle is:
Reasoning: One horizontal, one slanted line.
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Which case gives maximum angle?
Reasoning: $90^{o}$ is maximum acute intersection angle.
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If denominator in formula becomes zero, angle is:
Reasoning: Condition of perpendicular lines.
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Angle between horizontal and vertical line is:
Reasoning: They are perpendicular.
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If slopes are $3$ and $- \ 1/3$, angle is:
Reasoning: Product $= - \ 1$
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Angle between lines is independent of:
Reasoning: Distance does not affect angle.
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If angle between lines is $0^{o}$, lines are:
Reasoning: No angle $\Longrightarrow$ parallel lines.
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If angle is $180^{o}$, lines are:
Reasoning: Collinear but opposite direction.
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Which value is used in angle formula?
Reasoning: Formula uses slopes only.
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Angle between two lines is acute when:
Reasoning: Condition for acute angle.
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Angle becomes obtuse when:
Reasoning: Negative relation gives obtuse angle.
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If one slope is undefined, angle is measured between:
Reasoning: Vertical vs horizontal gives $90^{o}$.
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Angle between lines depends on:
Reasoning: Only direction matters.
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If slopes are $0$ and $- \ 1$, angle is:
Reasoning: Horizontal and slanted line.
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Reasoning: We take smallest angle of intersection.
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