6.3: Types of Quadrilaterals - Arrowhead High School

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Define and draw the following Quadrilaterals: 1. Parallelogram: Opposite sides of the quadrilateral are parallel. 2. Rhombus: All four sides of a quadrilateral areΒ ...
6.3: Types of Quadrilaterals

Brinkman Geometry

1. Warm up proof!

A

Given: βˆ†π΄π΅πΆ 𝑖𝑠 π‘–π‘ π‘œπ‘ π‘π‘’π‘™π‘’π‘ . Prove: ∠5 β‰… ∠4. Conclusion

1

Justification 5

2

3 4 C

βˆ†π΄π΅πΆ 𝑖𝑠 π‘–π‘ π‘œπ‘ π‘π‘’π‘™π‘’π‘ .

Given

∠2 β‰… ∠3

Isosceles Triangle Base Angles Theorem

π‘šβˆ 3 + π‘šβˆ 4 = 180

Definition of Linear Pair

π‘šβˆ 2 + π‘šβˆ 5 = 180

Definition of Linear Pair

π‘šβˆ 3 + π‘šβˆ 5 = 180

Substitution Property of Equality

∠5 β‰… ∠4

Addition Property of Congruence

B

Define and draw the following Quadrilaterals: 1.

Parallelogram: Opposite sides of the quadrilateral are parallel.

2. Rhombus: All four sides of a quadrilateral are congruent.

3. Rectangles: A quadrilateral comprised of 4 right angles.

4. Square: A quadrilateral with all four sides congruent and four right angles.

5. Kite: A quadrilateral with 2 distinct pairs of congruent consecutive sides.

6. Trapezoid: A quadrilateral with at least one pair of parallel sides.

7. Isosceles Trapezoid: A quadrilateral with a pair of base angles that have the same measure and the sides opposite of the base angles are congruent. Time to think! 6. Is a parallelogram a rhombus? Explain! No, there must be four equal sides!

7. Is a rectangle a rhombus? Explain! No, not all four sides have to be congruent. 8. Is a rhombus a rectangle? Explain! No, there needs to be 4 right angles. 9. Is a square a rectangle? Explain! Yes, there are four right angles. 10. Is a rectangle a square? Explain! No, only if all four sides are congruent. 11. Is a rectangle a parallelogram? Explain! Yes, there are two pairs of parallel sides. Proof time! Given: 𝑃𝑂//𝐴𝑅 , and 𝑃𝐴 β‰… 𝑂𝑇. βˆ†π‘‚π‘‡π‘… 𝑖𝑠 π‘–π‘ π‘œπ‘ π‘π‘’π‘™π‘’π‘  π‘€π‘–π‘‘β„Ž π‘£π‘’π‘Ÿπ‘‘π‘’π‘₯ 𝑂. Prove: 𝑃𝑂𝑅𝐴 is an isosceles trapezoid. Conclusion 1. 𝑃𝑂//𝐴𝑅 π‘Žπ‘›π‘‘ 𝑃𝐴 β‰… 𝑂𝑇

Justification Given

2. βˆ†π‘‚π‘‡π‘… 𝑖𝑠 π‘–π‘ π‘œπ‘ π‘π‘’π‘™π‘’π‘  π‘€π‘–π‘‘β„Ž Given π‘£π‘’π‘Ÿπ‘‘π‘’π‘₯ 𝑂. 3. OT = OR Definition of Isosceles Triangle 4. PA = OR

Transitive Property of Equality

5. PORA is an isosceles trapezoid

Definition of Isosceles Trapezoid

12. Draw the hierarchy of quadrilaterals below.

6.3 Worksheet Given below is a chart with five columns: rectangle, parallelogram, square, rhombus, and isosceles trapezoid. Which of the 11 properties listed below are true for the five quadrilaterals? Fill in the following chart with yes or no for each of the 11 properties.

1 2 3 4 5 6 7 8 9 10 11 6. At least one pair of opposite sides is congruent.

1. Opposite sides are parallel

5. Has four right angles. 3. Opposite sides are congruent. 8. When sides are congruent, diagonals bisect each other.

2. Opposite angles are β‰…. 4. All sides are congruent. 10. Diagonals are angle bisectors.

9. Diagonals are perpendicular.

7. Diagonals are congruent.

11. Diagonals are lines of symmetry.