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Understanding Trapezoids and Kites: Properties and Theorems in Geometry

This section delves into trapezoids and kites, key shapes in geometry. A trapezoid has one pair of parallel sides, with aspects like bases and legs discussed. Theorems highlight properties of isosceles trapezoids, such as congruent legs and base angles, plus equal diagonals. The midsegment of a trapezoid, which connects leg midpoints, is also explored. Kites, characterized by two pairs of congruent consecutive sides, have specific properties, including perpendicular diagonals. This resource is essential for mastering geometry concepts related to these quadrilaterals.

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Understanding Trapezoids and Kites: Properties and Theorems in Geometry

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  1. Trapezoids and Kites Chapter 6 Section 6 Tr

  2. Trapezoid • A quadrilateral with exactly one pair of parallel sides

  3. Parts of a Trapezoid Base Leg Leg Base Angle Base Angle Base

  4. Isosceles Trapezoid • A trapezoid with congruent legs and congruent base angles.

  5. Theorem 6-19 • If a quadrilateral is an isosceles trapezoid, then each par of base angles is congruent.

  6. Turn to Page 390 • Look at Problems 1 and 2 • Try the Got It Problems for those examples.

  7. Theorem 6-20 • If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.

  8. Midsegment of a Trapezoid • The segment that joins the midpoints of the legs.

  9. Theorem 6-21 • If a quadrilateral is a trapezoid, then • The midsegment is parallel to the bases • The length of the midsegment is half the sum of the lengths of the bases.

  10. Turn to Page 391… • Look at Problem 1 • Try the Got It Problems for that example.

  11. Kite • Quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.

  12. Theorem 6-22 • If a quadrilateral is a kite, then its diagonals are perpendicular.

  13. Turn to Page 393… • Look at Problem 4 • Try the Got It for that problem.

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