1. 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

2. 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.

3. 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.

4. 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.

5. 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.

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

7. 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.

8. 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.

9. 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.

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

11. 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.

12. 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 and 5x Find the length of the side of the parallelogram represented by 4x - 1.

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

14. 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.

15. 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

16. 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