Respuesta :
Answer: Rectangle and Trapezium
Step-by-step explanation:
If you have the slopes, then you can tell when two lines are parallel.
A rectangle has two pairs of parallel sides
A trapezium has exactly one pair of parallel sides
1.
We can determine whether a quadrilateral is a rectangle or a trapezium using the slope and the properties of parallel and perpendicular lines.
2.
How are the slopes of perpendicular sides related?
Product of the slopes of perpendicular lines = -1.
M₁ * M₂ = -1 .
How are the slopes of parallel sides related?
Slopes of parallel lines are equal.
M₁ = M₂.
How do we determine a rectangle?
Suppose we have a quadrilateral ABCD.
AB and CD are one pair of opposite sides.
BC and DA are another pair of opposite sides.
AB is adjacent to BC. BC is adjacent to CD. CD is adjacent to DA. DA is adjacent to AB.
Slope AB = M₁
Slope BC = M₂
Slope CD = M₃
Slope DA = M₄
For ABCD to be a rectangle, by properties opposite sides need to be parallel and adjacent sides need to be perpendicular.
∴ If M₁ = M₃, M₂ = M₄ (for opposite sides to be parallel)
and if M₁.M₂ = -1, M₂.M₃ = -1, M₃.M₄ = -1, and M₄.M₁ = -1 (for adjacent sides to be perpendicular) then the given quadrilateral ABCD is a rectangle.
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