# MUHAMMET ARICAN

# Georgia Performance Standards for This Topic:

MM1G1. Students will investigate properties of geometric figures in the coordinate plane.

a. Determine the distance between two points.

b. Determine the distance between a point and a line.

c. Determine the midpoint of a segment.

d. Understand the distance formula as an application of the Pythagorean

theorem.

e. Use the coordinate plane to investigate

**MM1G3.** Students will discover, prove, and apply properties of triangles,quadrilaterals, and other polygons.

a. Determine the sum of interior and exterior angles in a polygon.

b. Understand and use the triangle inequality, the side-angle inequality, and the

exterior-angle inequality.

c. Understand and use congruence postulates and theorems for triangles (SSS,

SAS, ASA, AAS, HL).

d. Understand, use, and prove properties of and relationships among special

quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

e. Find and use points of concurrency in triangles: incenter, orthocenter,

circumcenter, and centroid.

### Day 1: Students will learn **constructing a segment of length √x by using compass and straightedge**.

### Day 2 : Students will apply **Pythagorean Theorem **to calculate the length of the segment and answer exercise questions.

### Day 3 : Students will **learn how to construct a segment with a length of (1+√5)/2 which is equal to the Golden Ratio.**

### Day 4 : Students will **construct a regular pentagon with a side of 1 unit.**

### A GSP demonstration for regular pentagon with a length of 1 unit: Regular Pentagon

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