Download Important Vocabulary…

Ben Petersen
Math Endorsement
Bethel School District, Willamette High School, Mr. Hatefi
Geometry Unit Plan for February 6th – March 10th
Ratios and Proportions of Similar Polygons
Properties of Right Triangles
2nd period
Chapter 8:
Important Vocabulary…
Ratio:
Proportion:
Means:
Extremes:
Geometric Mean:
Similar Polygons:
Scale Factor:
The quotient of two numbers that are measured in the same units a/b.
(8.1)
An equation that equates two ratios is a proportion. a/b = c/d
(8.1)
b and c are means.
(8.1)
a and d are extremes.
(8.1)
Is the positive number x such that a/x = x/b, where x= (a*b)^1/2
(8.2)
Corresponding angles are congruent between two figures and their
corresponding sides are all of equal proportion
(8.3)
If two polygons are similar then the ratio of the lengths of corresponding
sides is called the scale factor
(8.3)
Lesson Plans Objectives:
 Pre-assessment: Chapter 8 Prerequisite Skills Review, refer to CRB pgs 5-6
 Lesson 8.1 (HW: 10-44 even,45-50,51-53,54-58 even,62-66,68-72 even)
 Students will find and simplify the ratio of two numbers (simple knowledge)
 Students will use proportions to solve real-life problems (application)
 Students will redefine “cross product property” and “reciprocal property” in their own words
(willingness to try)
 Students will convert similar units before finding ratios and proportions (simple knowledge)
 Lesson 8.2 (HW: 10-28 even,33-37)
 Students will define and use properties of proportions (algorithmic skill, simple knowledge)
 Students will use proportions to solve real-life problems (application)
 Students will use cross products and ratios to solve proportional problems (algorithmic skill)
 Lesson 8.3 and 8.4 (8-18 even, 19-28, 39-42; 18-26 even, 33-38, 40-44 even)
 Students will identify similar polygons (simple knowledge)
 Students will discover what properties makes polygons similar to each other (discover a
relationship)
 If given that two polygons are similar, then students will find the missing side lengths using
proportions (application).
 Students will use the Angle-Angle Postulate to discover when two triangles are similar (discover,
simple knowledge)
 Students will discover “why a line has only one slope” (willingness to try, Example 3)
 8.1-8.3 Quiz



Lesson 8.5 (HW: 1-14)
 Students will use SSS and SAS Similarity Theorems to identify similar triangles (algorithmic
skill)
 Students will use similar triangles to solve real-life problems (application)
Lesson 8.6 (HW: 11-39,41-53)
 Students will use the Triangle Proportionality Theorems to calculate segment lengths
(algorithmic skill)
 Students will use proportionality theorems to solve real-life problems (application)
Chapter 8 Unit Quiz
Chapter 9:
Important Vocabulary…
Pythagorean Triple:
Special Right Triangles:
Trigonometric Ratio:
Angle of Elevation:
Solve a Right Triangle:
Magnitude of a Vector:
Direction of a Vector:
Sum of Two Vectors:
Is a set of three positive integers that satisfy the equation c^2 = a^2
+ b^2
(9.2)
Right triangles who angle measures are 45,45,90 or 30,60,90
(9.4)
Is the ratio of the lengths of two sides of a right triangle, sin, cosine
and tangent
(9.5)
Is the angle your line hypotenuse makes with the horizontal leg
(9.5)
Means to determine the measure of all six parts of a right triangle,
you need “two side lengths” or “one side and one acute angle” to
solve
(9.6)
Is the distance from the initial point to the terminal point
(9.7)
Is determined by the angle a vector makes with a horizontal line
(9.7)
u=<a,b> and v=<c,d> ; u + v = <a+c,b+d>
Lesson Plans Objectives:
 Chapter 8 Assessment Review
 Lesson 9.1 (HW: 11-30,33-36,41,42,44-50 even)
 Students will solve problems involving similar right triangles formed by the altitude drawn to the
hypotenuse of a right triangle (simple knowledge)
 Students will use a geometric mean to solve problems (application)
 Given 3 similar triangles and unknowns, the student will correctly setup proportions to solve for
missing parts of the triangles for 2 of them (application)
 Lesson 9.2 and 9.3 (HW: 7-18, 25-33 odd; 1-6, 14-28 even)
 Students will attempt to prove the Pythagorean Theorem (willingness to try)
 Students will use and apply the Pythagorean Theorem to solve real-life problems (application,
algorithmic skill)
 Students will use the Converse of Pythagorean Theorem to show that a triangle is right
(algorithmic skill)
 Students will use the Pythagorean Inequalities to identify acute or obtuse triangles (application)
 Students will find when 3 sides cannot create a triangle (simple knowledge)
 9.1 – 9.3 Quiz
 Lesson 9.4 (HW: 2-28 even)
 Students will discover the properties of 30,60,90 and 45,45,90 triangles (discover a relationship)



 Students will find the lengths of special right triangles (simple knowledge)
 Students will use special right triangles to solve real-life problems (application)
Lesson 9.5 (HW: 10-38 even, 11-39 odd, 40-44, 47-51)
 Students will use, define, and find the sine, cosine, and tangent, of an acute angle (simple
knowledge)
 Students will use trigonometric ratios to solve real-life problems (application)
Lesson 9.6 (HW: 12-32, 34-40, 42-45)
 Students will solve right triangles, by finding the six parts of the triangle (algorithmic skill)
 Given 2 known sides of a right triangle students will solve for the six parts
 Given 1 angle and 1 side of a right triangle, students will solve for the six parts
 Students will use right triangles to solve real-life problems (application)
 Students will solve 5 out of 7 right triangle problems (algorithmic skill)
Chapter 9 Unit Quiz