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Unit 7

Unit Overview

In this unit, students formalize their understanding of similarity, which was informally studied prior to geometry. Students investigate and apply dilations of polygons in the coordinate plane. Similarity of polygons and triangles are explored. Triangle similarity postulates and theorems are formally proven. The proportionality of corresponding sides of similar figures is applied. Similarity is extended to the side-splitting, proportional medians, altitudes, angle bisectors, and segments theorems. The geometric mean is defined and related to the arithmetic mean. Ratios of areas and volumes of similar solids are studied. The effect that a change in the linear dimensions of a solid has on the surface area and volume of the solid is explored.

Honors students will also explore the Golden Ratio and its applications, as well as the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle. This unit includes an optional enrichment section on fractals.

Instructional Flow

Instructional Flow (PDF)
Description of the typical order of textbook sections and topics taught in the unit.

Expectations, Essential Questions, Enduring Understandings and Vocabulary

Unit 7 Standards for Geometry(PDF)
Explanation of what your child should understand by the end of each unit (enduring understandings), how he/she will get to that understanding (essential questions), and how he/she will be evaluated (indicators).

Content Map

Content map for Geometry Unit 7 (PDF)

Web Resources

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