Skip to main content

Unit 5

Unit Overview

In the first part of this unit (5A) students compute the perimeter and area of polygons and circles. Students have been studying these formulas since elementary school. The emphasis in this unit is on proving the formulas. Students determine the areas of composite figures by addition and subtraction in problem-solving situations. Students learn about radical expressions with non-perfect square integer radicands, as well as radicals containing fractions. They also develop and apply the product and quotient properties of radicals. Applications of the Pythagorean theorem and its converse, Pythagorean triples and Pythagorean inequalities are explored. The special right triangles of 30-60-90 and 45-45-90 are also studied and are applied to determine the area of regular polygons.

In the second part of this unit (5B), They derive and apply the distance formula. Students prove theorems involving midpoints and slopes using coordinate geometry. They compute probabilities based on using the ratios of areas of figures. Honors students study a non-Euclidean geometry known as taxicab geometry. In an optional section, honors students explore the method of quadrature that is used to estimate the area of figures bounded by curves.

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 5 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 5 (PDF)

Web Resources

No content

Unit 1  Unit 2  Unit 3  Unit 4  Unit 5  Unit 6  Unit 7  Unit 8  Unit 9