Lesson 4: Properties of Polygons

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Presentation transcript:

Lesson 4: Properties of Polygons 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

Lesson 4: Properties of Polygons Unit 6: Geometry 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.

Lesson 4: Properties of Polygons Unit 6: Geometry 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.

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

Lesson 4: Properties of Polygons Unit 6: Geometry 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.

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

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

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

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

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

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

Lesson 4: Properties of Polygons Unit 6: Geometry Lesson 4: Properties of Polygons Example #1: The opposite sides of a parallelogram are represented by 2x + 10 and 5x - 20. Find the length of the side of the parallelogram represented by 4x - 1.

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

Lesson 4: Properties of Polygons Unit 6: Geometry 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.

Lesson 4: Properties of Polygons Unit 6: Geometry 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 6 4 B E 5 C D

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