Advanced Geometry Polygons Lesson 4

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Presentation transcript:

Advanced Geometry Polygons Lesson 4 Other Quadrilaterals

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

Characteristics of Rhombi 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.

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

Kites two distinct pairs of adjacent congruent sides

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

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

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.

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

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

Use rhombus LMNP and the given information to 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.

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.

Given each set of vertices, determine whether 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.

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