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Unit 6: Geometry

Lesson 4: Properties of Polygons. Learning Goal I can use the properties of polygons to find unknown side lengths and missing angle measurements. Unit 6: Geometry. Lesson 4: Properties of Polygons. New Terms Midpoint: The middle of a side on a polygon

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Unit 6: Geometry

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  1. Lesson 4: Properties of Polygons • Learning Goal • I can use the properties of polygons to find unknown side lengths and missing angle measurements Unit 6: Geometry

  2. Lesson 4: Properties of Polygons New Terms Midpoint: The middle of a side on a polygon Midsegment: A line that joins the midpoints of two adjacent sides Inscribed Polygon: A polygon made entirely of midsegments. It is inside the original polygon. Unit 6: Geometry

  3. Lesson 4: Properties of Polygons New Terms Diagonal:Two lines that criss-cross inside a quadrilateral, each spanning from one vertex to the opposite vertex. Bisect: To split a line segment into two equal parts. Unit 6: Geometry

  4. Lesson 4: Properties of Polygons The inscribed polygon will have the same number of sides as the outer, original polygon. Unit 6: Geometry A regular polygon will produce a regular inscribed polygon.

  5. Lesson 4: Properties of Polygons With a triangle, each midsegment created will be parallel to the opposite side of the triangle, and exactly half its length. Unit 6: Geometry

  6. Lesson 4: Properties of Polygons With a quadrilateral, the midsegments will form a parallelogram. Unit 6: Geometry

  7. Lesson 4: Properties of Polygons The diagonals of a square bisect each other at right angles and are equal in length. Unit 6: Geometry

  8. Lesson 4: Properties of Polygons The diagonals of a rhombus bisect each other at right angles and bisect the angles at the vertices. Unit 6: Geometry

  9. Lesson 4: Properties of Polygons The diagonals of a rectangle bisect each other and are equal in length. Unit 6: Geometry

  10. Lesson 4: Properties of Polygons The diagonals of a parallelogram bisect each other. Unit 6: Geometry

  11. Lesson 4: Properties of Polygons The diagonals of a kite bisect each other at right angles. Therefore they are perpendicular to each other. Unit 6: Geometry

  12. Lesson 4: Properties of Polygons Example #1:The opposite sides of a parallelogram are represented by2x + 10 and 5x - 20. Find the length of the side of the parallelogram represented by 4x - 1. Unit 6: Geometry

  13. Lesson 4: Properties of Polygons Example #2: In rhombus MATH, MH = y + 8 and HT = 4y - 7. Find MA. Unit 6: Geometry

  14. Lesson 4: Properties of Polygons Example #3:In rectangle ABCD, the diagonals intersect at E. If AE = 3x + y, BE = 4x - 2y, and CE = 20, find x and y. Unit 6: Geometry

  15. Lesson 4: Properties of Polygons If B and E are the midpoints of AC and AD respectively, find the length of CD and angle AEB. A Unit 6: Geometry 6 4 B E 5 C D

  16. Lesson 4: Properties of Polygons • Practice • Page 378 Q#5, 6, 7, 8, 9, 11 • Quiz Tomorrow! Angle Properties and Pythagorean Theorem Unit 6: Geometry

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