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Quadrilateral Investigation

matthew.hardie, Bradford L Dalton, Mar 21, 2023

This investigation is about discovering the relationships between sides, angles, and the diagonals of the: square, rectangle, rhombus, parallelogram, kite, and isosceles trapezoid. Try to discover which lengths are congruent, parallel, perpendicular, or bisected. Discover which angles are congruent, complementary, supplementary, or bisected. Try to generalize your findings by using descriptions like opposite or consecutive with what and how many that applies to. For example a generalization might be: “One pair of opposite sides are parallel.” On the polygon put markings of congruency, right angles, or parallel for the sides or angles.

1. Kite - measurements(B)
2. Isosceles Trapezoid - measurement(B)
3. Paralellogram - measurements(B)
4. Rectangle - measurements(B)
5. Rhombus - measurement(B)
6. Square - measurements(B)

1.

Kite - measurements(B)

Go Fly a ....

This investigation is about discovering the relationships sides, angles, and the diagonals of the kite. Try to discover which lengths are congruent, parallel, perpendicular, or bisected. Discover which angles are congruent, complementary, supplementary, or bisected. Try to generalize your findings by using descriptions like opposite or consecutive with what and how many that applies to. For example a generalization might be: “Kites have ______________pairs of adjacent, congruent sides.” On the polygon put markings of congruency, right angles, or parallel for the sides or angles.

Kite - measurements

Explain all using complete sentences

1. Are any of the sides parallel? Which pairs?[br]

[br][br] [br]2. Are any of the sides perpendicular? Which pairs?[br]

[br]3. Are any of the sides congruent? Which pairs?[br]

4. Are any of the angles congruent? Which pairs?[br][br]

[br][br]5. Are any of the angles supplementary? Which pairs?[br]

[br][br]6. Are the diagonals congruent?[br]

7. Do the diagonals bisect each other?

[br][br]8. Do the diagonals bisect opposite angles? [br]

9. Are the diagonals perpendicular?

Summary

Why is a kite a kite? [br][br]What makes it unique?

Multiple choice or T/F

A kite is a [url=https://www.cuemath.com/geometry/quadrilaterals/]quadrilateral[/url] that has two pairs of consecutive equal sides and perpendicular diagonals.

True False

Since a kite has perpendicular diagonals then.....

They have the same slopes The slopes must be negative reciprocals Are always equal in length They intersect at 60 degree angles

Can a kite have sides of 12 units, 25 units, 13 units, and 25 units?[br]

True False

Select all possible correct answers

The diagonals of a kite.

The diagonals of a kite intersect each other at right angles. It can be observed that the longer diagonal bisects the shorter diagonal. Always have the same length Has exactly one diagonal The two diagonals are not of the same length.

– Bradford L Dalton, matthew.hardie

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