Properties and Slopes of Quadrilaterals

Mr. Allen guides students through finding the coordinates of point C to form a rectangle ABCD. He explains the properties of rectangles, such as right angles and congruent sides, and demonstrates how to calculate slopes to identify perpendicular lines. By using these concepts, he locates point C and verifies the rectangle's properties, ensuring opposite sides are parallel and congruent.

What is one of the key properties of a rectangle?

• All angles are right angles

• All sides are parallel

• Diagonals are perpendicular

• All sides are equal

How do you calculate the slope between two points?

• Divide the difference in x-coordinates by the difference in y-coordinates

• Multiply the x-coordinates and y-coordinates

• Divide the difference in y-coordinates by the difference in x-coordinates

• Add the x-coordinates and y-coordinates

What is the slope of a line that goes up 6 units and over 8 units?

• 4/3

• 8/6

• 3/4

• 6/8

What indicates that two lines are perpendicular?

• They have the same slope

• Their slopes are opposite reciprocals

• They are parallel

• They intersect at a 45-degree angle

If a line goes down 4 units and to the right 3 units, what is its slope?

• -3/4

• 3/4

• -4/3

• 4/3

How can you find the coordinates of point C in a rectangle?

• By guessing its position

• By using the same slope as another line segment

• By using the midpoint formula

• By measuring the distance from point A

What is the coordinate of point C if you go up 6 units and right 8 units from point D?

• (8, 6)

• (5, 2)

• (2, 5)

• (6, 8)

What property ensures that opposite sides of a rectangle are congruent?

• They intersect at right angles

• They are perpendicular

• They are parallel

• They have the same length

What is the significance of opposite reciprocal slopes in a rectangle?

• They indicate parallel lines

• They indicate congruent sides

• They indicate perpendicular lines

• They indicate equal angles

What does it mean if a quadrilateral has opposite sides that are both parallel and congruent?

• It is a rhombus

• It is a trapezoid

• It is a parallelogram

• It is a square