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Mr. Wolf
Tuesday 12/9/08
Geometry
Grades 10-12
Unit 7: Right Triangles
Review Unit 7
Materials and Resources:
 Warm-up (1 per student)
 Unit 7 Study Guide sheet (1 per student)
 Unit 7 Review Bingo sheet (1 per student)
 Exit Ticket (1 per student)
PA Standards Addressed:
Instructional Objectives:
 Students will be able to review material from Unit 7 by completing a review
activity.
Time
10 min
1 min
1 min
25 min
Activity
Warm-up
Agenda
Homework Check
Review Homework
50 min
Review Unit 7
1 min
5 min
Agenda
Conclusion
Homework:
Online Quiz #12
Lesson Reflection:
Description
Pass out the Warm-up and review solutions.
Review the goals for the day.
Spot-check and review solutions
Present the HW solutions and answer any
questions.
Modeling:
Guiding:
Independent Practice:
Assessment:
Modifications:
Students with special needs…
Advanced students…
Revisit goals and identify whether they were met.
Pass out the Exit Ticket and collect at the bell.
Geometry Fall 2008
Name: ________________________
Warm-up
In Greek mythology, Sisyphus was condemned to an eternity of rolling an enormous
bolder up a hill, only to watch it roll back down again. The angle of elevation of the hill
is 35° and the peak of the hill is 325 feet above the ground level. Draw a diagram to
illustrate this scenario and calculate the distance Sisyphus must roll the boulder.
Geometry Fall 2008
Name: ________________________
Warm-up
In Greek mythology, Sisyphus was condemned to an eternity of rolling an enormous
bolder up a hill, only to watch it roll back down again. The angle of elevation of the hill
is 35° and the peak of the hill is 325 feet above the ground level. Draw a diagram to
illustrate this scenario and calculate the distance Sisyphus must roll the boulder.
Geometry Fall 2008
Name: ________________________
Unit 7 Study Guide
Section 8.1 Similarity in Right Triangles
 Solve and simplify radical expressions (square roots)
 Find the geometric mean between two numbers
 Set up geometric mean statements and proportions and solve for unknown values
in right triangles
Section 8.2 The Pythagorean Theorem
 State and prove the Pythagorean Theorem
 Apply the Pythagorean Theorem to right triangles in order to find missing side
lengths
Section 8.3 The Converse of the Pythagorean Theorem
 State the Converse of the Pythagorean Theorem
 Determine whether a triangle is right, acute, or obtuse by applying the
Pythagorean Theorem, Acute Triangle Theorem, and Obtuse Triangle Theorem
 Determine whether or not a triangle can exist based on given side lengths
Section 8.4 Special Right Triangles
 Calculate missing side lengths of 45°-45°-90° and 30°-60°-90° triangles
Section 8.5 & 8.6 The Sine, Cosine, & Tangent Ratios
 Evaluate trigonometric functions using a calculator
 Apply SOHCAHTOA to right triangles in order to set up sin, cos, and tan ratios
 Use the sin, cos, and tan ratios to determine missing side lengths in triangles
 Evaluate inverse trigonometric functions using a calculator
 Use the inverse trigonometric functions to determine missing angle measures in
triangles
Section 8.7 Real World Applications
 Apply right triangle trigonometry (sin, cos, tan) to real world situations
Geometry Fall 2008
Name: ________________________
Unit 7 Review Bingo
Directions: Solve the following problems and choose 24 of your solutions to place in the
boxes of the BINGO board in any order you choose.
Section 8.1 Similarity in Right Triangles
Directions: Simplify the following radical expressions (square roots). Be sure to fully
simplify your answer.
5
=
5 2=
121 =
6
14  2 =
40 =
72 =
10  3 =
32
4
8
=
10
=
Directions: Find the geometric mean between the given numbers. Be sure to fully
simplify your answer.
The geometric mean between 6 and 9 = _______
The geometric mean between 4 and 5 = _______
The geometric mean between 8 and 7 = _______
Directions: Set up geometric mean statements and proportions to solve for x, y, and z. Be
sure to fully simplify your answer.
Section 8.2 The Pythagorean Theorem
Directions: Apply the Pythagorean Theorem to find the missing side lengths.
Section 8.3 The Converse of the Pythagorean Theorem
Directions: Determine whether the triangle with the given dimensions is right, acute,
obtuse, or “does not exist.”
8, 14, 17
__________
8, 8 3 , 16
__________
4, 9, 15
__________
5, 6, 7
__________
Section 8.4 Special Right Triangles
Directions: Calculate missing side lengths of the triangles.
Section 8.5 & 8.6 The Sine, Cosine, & Tangent Ratios
Directions: Evaluate the following trigonometric functions using a calculator. Round
answers to the nearest hundredth.
sin( 52) 
cos( 25) 
tan( 70) 
Directions: Evaluate the following inverse trigonometric functions using a calculator.
Round answers to the nearest whole number.
sin 1 (0.9962) 
1
cos 1   
2
2 7

tan 1 

5


Directions: Apply SOHCAHTOA to the right triangle in order to evaluate the sin, cos,
and tan functions. Be sure to fully simplify and rationalize your answer.
sin(  ) 
cos( ) 
tan( ) 
Directions: Use the sin, cos, and tan ratios to determine the missing side lengths in the
triangles. Round answers to the nearest hundredth.
Directions: Use the inverse trigonometric functions to determine the missing angle
measures. Round answers to the nearest whole number.
Section 8.7 Real World Applications
A sailboat 10 miles due north of the coast is approaching a dangerous rip tide. A harbor
patrol station on the coast is aware of the rip tide and has calculated that it is 27 miles
from the patrol station. If the boat comes within 30 miles of the rip tide, the patrol station
must send out an emergency radio frequency to warn the boat.
Fill in the above information into the
diagram at right and calculate the angle θ
(to the nearest whole number) and the
distance d (round to the hundredths)
between the sailboat and the rip tide.
θ=
d=
Should the patrol station send out an
emergency radio warning?
FREE
SPACE
Geometry Fall 2008
Name: ________________________
Exit Ticket
Proof of the Pythagorean Theorem:
Given: ACB is a right angle.
Prove: a 2  b 2  c 2
Statements
Reasons
1)
1)
2)
2)
3)
3)
4)
4)
5)
5)
6)
6)
Geometry Fall 2008
Name: ________________________
Exit Ticket
Proof of the Pythagorean Theorem:
Given: ACB is a right angle.
Prove: a 2  b 2  c 2
Statements
Reasons
1)
1)
2)
2)
3)
3)
4)
4)
5)
5)
6)
6)