(July 2013)
Unit Statement: This unit defines and examines special segments in triangles and the relationships they create. Concepts are developed involving inequalities in both one and two triangles. In addition, the method of indirect proof is presented.
Essential Outcomes: (must be assessed for mastery)
Problem solving and higher order thinking components are essential for ‘A’ level
mastery. Each outcome can contain problem solving and higher order thinking components (as found in suggested text).
1.
T he S tudent W ill apply theorems about perpendicular bisectors (5.1 pp 312 - 318).
2.
TSW apply the properties of perpendicular bisectors and angle bisectors of a triangle (5.2 pp.319 - 325).
3.
TSW apply the properties of medians and altitudes of a triangle (5.3 pp. 326 -
331).
4.
TSW apply the properties of triangle midsegments (5.4 pp. 334 - 339).
5.
TSW write indirect proofs and apply inequalities in a single triangle (5.5 pp. 344 - 351).
6.
TSW solve problems involving inequalities in two triangles (5.6 pp. 352 - 357).
7.
TSW apply the Pythagorean Theorem and its converse to solve problems (5.7 pp.
360 - 367).
8.
TSW justify and apply the properties of 45-45-90 and 30-60-90 triangles (5.8 pp.
368 – 374).
Introduced and Practiced Outcomes: (taught not assessed)
1. T he S tudent W ill justify the Pythagorean Theorem by building figures and comparing their areas (5.6 p. 359).
Key Terms and Concepts:
Altitude
Equidistant
Median centriod incenter midsegment circumcenter indirect proof orthocenter circumscribed inscribed concurrency concurrent locus
Pythagorean triple
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QSI GEOMETRY SEC E05
Copyright © 1988-2013

Suggested Assessment Tools and Strategies:
Attached Rubric or teacher generated rubric that assesses ALL essential outcomes
(TSWs).
Suggested Resources:
Holt McDougal Geometry, Chapter 5, Sections 1 - 8.
Holt McDougal Geometry, Problem Solving Workbook
Holt McDougal Geometry, Practice Worksheets
Holt McDougal Geometry, Reading Strategies
Holt McDougal Geometry, Reteach Worksheets
Holt McDougal Geometry, Challenge Worksheets
Holt McDougal Geometry, Assessment Resources
Technology Links:
Holt McDougal Geometry, Online Edition, 6-year subscription
Holt McDougal Geometry, Interactive Answers and Solutions CD-ROM
Holt McDougal Geometry, Lesson Tutorial Videos DVD-ROM
Holt McDougal Geometry, Teacher One-Stop DVD
On Core Mathematics Deluxe Eamview Grades 6-12 CD-ROM
On Core Mathematics High School Activity Generator CD-ROM
Follett Destiny WebPath Express (found on school’s automated library system)
Tenmarks www.tenmarks.com/
Khan Academy https://www.khanacademy.org/
PhET Simulations http://phet.colorado.edu/en/simulations/category/math
EVALUATION RUBRIC FOUND ON FOLLOWING PAGE……………………..
QSI GEOMETRY SEC E05
Copyright © 1988-2013
19

Geometry
Essential Unit 5 (E05)

To receive a ‘B’, the student must show ‘B’ level mastery on all eight TSW’s.

To receive an ‘A’, the student must show ‘A’ level mastery in at least 4 of the 8 available TSW’s and ‘B’ level mastery on all of the remaining TSW’s.
TSW
1- apply the theorems about perpendicular bisectors.
‘A’ LEVEL
The student can theorems about
prove perpendicular bisectors.
‘B’ LEVEL
The student can
apply the theorems about perpendicular bisectors.
Notes
2- apply the properties of perpendicular bisectors and angle bisectors of a triangle.
The student can
prove properties of perpendicular bisectors and angle bisectors of a triangle.
The student can
apply the properties of perpendicular bisectors and angle bisectors of a triangle.
3- apply the properties of medians and altitudes of a triangle.
4- apply the properties of triangle midsegments.
The student can apply the properties of medians and altitudes to coordinate graphs where points consist of constant terms.
The student can
the apply properties of medians and altitudes of a triangle.
The student can come up with the different options for the third side of a triangle given an unspecified two sides and midsegment.
The student can
apply the properties of triangle midsegments.
5 write indirect proofs and apply inequalities in a single triangle.
The student can create original inequalities in a single triangle problem or apply it to regions on a map.
The student is able to write indirect proofs and apply inequalities in a single triangle.
6. solve problems
7. involving inequalities in two triangles.
apply the Pythagorean
Theorem and its converse to solve problems.
8. apply the properties of
45-45-90 and 30-60-90 triangles.
The student can solve multistep problems involving side lengths and angles of cubes and rectangles.
QSI GEOMETRY SEC E05
Copyright © 1988-2013
The student can apply the inequalities in two triangles to concentric circles and chords.
The student can analyze how
Pythagorean inequalities can be used to classify triangles as obtuse or acute.
The student can solve problems involving inequalities in two triangles.
The student can
apply the Pythagorean
Theorem and its converse to solve problems.
The student is able to apply the properties of
45-45-90 and 30-60-90 triangles.
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