Created on: April 29, 2015

Website Address: https://library.curriki.org/oer/Cluster--Use-coordinates-to-prove-simple-geometric-theorems-algebraically

TABLE OF CONTENTS

- Quiz - Connecting Algebra and Geometry through Coordinates Cluster: Use coordinates to prove simple geometric theorems algebraically: Standards: G.GPE.4. G.GPE.5, G.GPE.6, G.GPE.7
- G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.
- G.GPE.5 Prove the slope criteria for parallel and perpendicular lines
- G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

This unit has a close connection with the next unit. For example, a curriculum might merge G.GPE.1 and the Unit 5 treatment of G.GPE.4 with the standards in this unit. Reasoning with triangles in this unit is limited to right triangles; e.g., derive the equation for a line through two points using similar right triangles. Relate work on parallel lines in G.GPE.5 to work on A.REI.5 in High School Algebra I involving systems of equations having no solution or infinitely many solutions. G.GPE.7 provides practice with the distance formula and its connection with the Pythagorean theorem.

Standards: G.GPE.4. G.GPE.5, G.GPE.6, G.GPE.7

Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on the circle centered at the origin and containing the point (0, 2).

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.