/25 Math Chapter 8 : Topic 3 Triangle Angles by Slopes 1 / 25 The angle between two sides of a triangle is found using: A) Distance formula B) Midpoint formula C) Slope angle formula D) Intercept formula Reasoning: Angle between lines depends on slopes $\Longrightarrow$ $tan\ \theta =$ $\frac{m_{2}\ - \ m_{1}}{1\ + \ m_{1}\ m_{2}}$ 2 / 25 If slopes of two sides are equal, angle between them is: A) $0^{o}$ B) $90^{o}$ C) $45^{o}$ D) $180^{o}$ Reasoning: Equal slopes mean parallel lines. 3 / 25 If product of slopes is $- \ 1$, angle is: A) $0^{o}$ B) $90^{o}$ C) $180^{o}$ D) $45^{o}$ Reasoning: Perpendicular condition. 4 / 25 Angle between two sides is always: A) Largest angle B) Right angle C) Straight angle D) Smallest angle Reasoning: We take smaller angle at intersection. 5 / 25 If slops are $2$ and $3$, the angle is: A) Exactly $90^{o}$ B) $180^{o}$ C) Not $90^{o}$ D) $0^{o}$ Reasoning: Product $\neq - \ 1$, so not perpendicular. 6 / 25 Slope formula is used to: A) Find midpoint B) Find distance C) Find direction D) Find area Reasoning: Slope shows direction of line. 7 / 25 If one side is horizontal, its slope is: A) $0$ B) Negative C) Undefined D) $1$ Reasoning: No vertical change. 8 / 25 If one side is vertical, its slope is: A) Undefined B) $1$ C) $0$ D) Negative Reasoning: Division by zero occurs. $\Longrightarrow$ $\frac{1}{0} = \infty$ 9 / 25 Angle between horizontal and vertical sides is: A) $0^{o}$ B) $45^{o}$ C) $90^{o}$ D) $180^{o}$ Reasoning: They are perpendicular. 10 / 25 If slopes are $- \ 2$ and $1/2$, angle is: A) $180^{o}$ B) $90^{o}$ C) $45^{o}$ D) $0^{o}$ Reasoning: Product $= - \ 1$ 11 / 25 If slopes are both negative but unequal, triangle angle is: A) Always $180^{o}$ B) Always $90^{o}$ C) Depends on values D) Always $0^{o}$ Reasoning: Only product matters. 12 / 25 Angle formula involves: A) Difference of slopes B) Division of slopes C) Product of slopes D) Addition of slopes Reasoning: Difference appears in numerator. 13 / 25 If denominator becomes zero in angle formula, angle is: A) $0^{o}$ B) Undefined C) $90^{o}$ D) $45^{o}$ Reasoning: Perpendicular condition. 14 / 25 Triangle angles depend on: A) Midpoints B) Area C) Length only D) Slopes of sides Reasoning: Slopes define direction. 15 / 25 If all slopes are equal, triangle becomes: A) Right triangle B) Degenerate line C) Equilateral triangle D) Isosceles triangle Reasoning: Points lie on same line. 16 / 25 Slope determines: A) Perimeter B) Area only C) Direction of side D) Position Reasoning: Slope gives inclination. 17 / 25 Angle increases when slopes: A) Differ more significantly B) Become equal C) Become same sign D) Become zero Reasoning: Greater difference increases angle. 18 / 25 If slopes are $0$ and $0.5$, angle is: A) $90^{o}$ B) $45^{o}$ C) $0^{o}$ D) $180^{o}$ Reasoning: Horizontal and slanted line. 19 / 25 Angle between two sides is independent of: A) Slopes B) Distance C) Direction D) Coordinates Reasoning: Distance does not affect angle. 20 / 25 If slopes are reciprocal negatives, lines are: A) Coincident B) Parallel C) Curved D) Perpendicular Reasoning: Condition for right angle. 21 / 25 Triangle angle at vertex depends on: A) Base only B) Opposite slope only C) Area D) Adjacent slopes Reasoning: Two meeting sides define angle. 22 / 25 If slopes are equal magnitude but opposite sign, angle is: A) $0^{o}$ B) $45^{o}$ C) $180^{o}$ D) $90^{o}$ Reasoning: Product $= - \ 1$ 23 / 25 Which case gives maximum triangle angle? A) Perpendicular lines B) Zero slopes C) Equal slopes D) Parallel lines Reasoning: $90^{o}$ is maximum intersection angle. 24 / 25 Angle between sides is calculated using: A) Distance formula B) Trigonometry C) Slope formula D) Algebra only Reasoning: Uses tangent identity. 25 / 25 If triangle sides are collinear, angle is: A) $180^{o}$ B) $90^{o}$ C) Undefined D) $0^{o}$ Reasoning: No angle between same line. Your score is 0% Restart quiz
