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Other Quadrilaterals

Other Quadrilaterals. Advanced Geometry Polygons Lesson 4. Rectangles. four right angles. Characteristics of Rectangles. Diagonals are congruent. All characteristics of a parallelogram are still true. Rhombus. Plural: Rhombi. four congruent sides. Characteristics of Rhombi.

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Other Quadrilaterals

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  1. Other Quadrilaterals Advanced Geometry Polygons Lesson 4

  2. Rectangles four right angles Characteristics of Rectangles • Diagonals are congruent. • All characteristics of a parallelogram are still true.

  3. Rhombus Plural: Rhombi four congruent sides Characteristics of Rhombi • The diagonals are perpendicular. • Each diagonal bisects a pair of • opposite angles. • All characteristics of parallelograms apply.

  4. Squares both a rectangle and a rhombus Characteristics of Squares • All characteristics of a rectangle apply. • All characteristics of a rhombus apply. • All characteristics of a parallelogram apply.

  5. Kites two distinct pairs of adjacent congruent sides

  6. Trapezoids exactly one pair of parallel sides Parts of a Trapezoid bases – the parallel sides legs – the non-parallel sides base angles – a pair of angles that touch a base

  7. Isosceles Trapezoid congruent legs Characteristics of Isosceles Trapezoids • Each pair of base angles is congruent. • The diagonals are congruent.

  8. Median of a Trapezoid segment joins the midpoints of the legs 36 28 * The median is parallel to the bases. * The length of the median is half the sum of the bases.

  9. Example: Quadrilateral RSTU is a rectangle. If RT = 6x + 4 and SU = 7x – 4, find x.

  10. Example: Quadrilateral LMNP is a rectangle. If m∠MNL = 6y + 2, m∠MLN = 5x + 8, and m∠NLP = 3x + 2, find x.

  11. Example: Use rhombus LMNP and the given information to find the value of each variable. Find m∠PNL if m∠MLP = 64. Find y if m∠1 = y² - 54.

  12. Example: DEFG is an isosceles trapezoid with median a) Find DG if EF = 20 and MN = 34. b) Find m∠1, m∠2, m∠3, & m∠4, if m∠1 = 3x + 5 and m∠3 = 6x – 5.

  13. Example: Given each set of vertices, determine whether quadrilateral EFGH is a rhombus, a rectangle, or a square. List all that apply. Explain your reasoning.

  14. Show that if LNPR is a rectangle and , then . Given: Prove: Proof: Reasons: Statements:

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