Lesson 3 Prove It! Practice Understanding
Learning Focus
Prove quadrilaterals are parallelograms, rectangles, rhombi, or squares using coordinates.
Find the perimeter and area of a quadrilateral on the coordinate plane.
How do I use algebra to show that a quadrilateral is a parallelogram, a rectangle, a rhombus, or a square?
Open Up the Math: Launch, Explore, Discuss
In this task, you need to use all the things you know about quadrilaterals, distance, and slope to prove that the shapes are parallelograms, rectangles, rhombi, or squares. Be systematic, and be sure that you give all the evidence necessary to verify your claim.
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Is
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b.
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Is
b.
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Is
Ready for More?
How can you show that a quadrilateral is a square with the fewest steps?
Takeaways
Ways to use coordinates to prove quadrilaterals are parallelograms, rectangles, rhombi, or squares:
Lesson Summary
In this lesson, we used the distance formula, the midpoint rule, and the properties of slopes of parallel and perpendicular lines to determine if a given set of four points on a coordinate plane formed the vertices of a parallelogram, rectangle, rhombus, or square.
1.
Find the values that will make the equations true.
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b.
2.
How many combinations of values for
3.
Find the perimeter of pentagon