Unit 5

Relationships within Triangles

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WHY DO WE NEED TO LEARN THIS?

... because if you want to be an architect, builder or engineer, you'll need to understand this...

Lecture7: The Elements of Coplanar Force Resolution
n.b. you'll learn about vectors in your physics class

Lesson/Objective Supplemental Lessons On-line Practice Homework
5-1  Midsegments of Triangles

Objectives:  To use properties of midsegments to solve problems

ESSENTIAL UNDERSTANDING: There are TWO special relationships between the midsegment of a triangle and the third side of the triangle
 


VIDEO TUTORS

Using the Triangle Midsegment Theorem

Using the Triangle Midsegment Theorem to measure indirectly


LESSON QUIZ
hw #5-1 Due Fri Dec 7
pg 288-289 #1-6, 19-29 Odd

(Optional Challenge #46-48)

5-2  Perpendicular and Angle Bisectors

Objectives:  To use properties of perpendicular bisectors and angle bisectors

ESSENTIAL UNDERSTANDING: There is a special relationship between the points on a perpendicular bisector and the endpoints of the segment AND there is a special relationship between the points on an angle bisector and the sides of an angle.
 


VIDEO TUTORS

Applying the Perpendicular Bisector Theorem

Applying the Angle Bisector Theorem


LESSON QUIZ
hw #5-2 Due Tues Dec 11
Read Section 5-2
pg 296-298
#1-10, 16-22, 29-31
5-3  Bisectors in Triangles

Objectives:  To identify properties of perpendicular bisectors and angle bisectors

ESSENTIAL UNDERSTANDING: For ANY triangle, certain sets of lines are always concurrent. Two of these sets of lines are the perpendicular bisectors of the triangle's three sides and the bisectors of the triangle's three sides.
 


VIDEO TUTORS

Using concurrent lines

  hw #5-3 Due Thurs Dec 13
pg 305-307
#1-6 All, #7-29 Odd 

(Optional Challenge #30-32)

 

5-4  Medians and Altitudes

Objectives:  To identify properties of medians and altitudes of a triangle

ESSENTIAL UNDERSTANDING: A triangle's three medians are always concurrent AND a triangle's three altitudes are always concurrent.
 


VIDEO TUTORS

Finding the lengths of medians

Identifying medians and altitudes


LESSON QUIZ
hw #5-4 Due Mon Dec 17
pg 312-314
#1-13 All, #15-23 Odd, 29,30,35 


UNIT 5 QUIZ on Sections 5-1 thru 5-4:  Mon, Dec 17th

5-5  Indirect Proof

Objectives:  To use indirect reasoning to write proofs

ESSENTIAL UNDERSTANDING:  You can use indirect reasoning as ANOTHER METHOD of proof. It is sometimes called proof by contradiction.

 

 
LESSON QUIZ
hw #5-5
Due Weds Dec 19
pg 319-321 #4-9 (remember to start each phrase with the words "Assume temporarily..."
#14,15,22,23,29

pg 323 #1-17 Odd
5-6  Inequalities in One Triangle

Objectives:  To use inequalities involving angles and sides of triangles

ESSENTIAL UNDERSTANDING:  The angles and sides of a triangle have special relationships that involve inequalities.
 

 
LESSON QUIZ
hw #5-7
Due Weds, Jan 2
pg 328 #1-5 ALL, #7-31 Odd, 37, 43
5-7  Inequalities in Two Triangles

Objectives:  To apply inequalities in two triangles

ESSENTIAL UNDERSTANDING: In triangles that have two pairs of congruent sides, there is a relationship between the included angles and the third pair of sides.
 

    hw #5-7
Due Friday Jan 4th
pg 336-338
#1-10 ALL, 11-23 Odd

Suggested Chapter 5 Review
Gosh, all of the problems look so yummy!!
Please browse the Chapter Review and try to find a problem or two that YOU DON'T LIKE!!
Report it back to me and we will review it in class!!

UNIT 5 REVIEW  
CHAPTER TEST
 
UNIT 5 TEST:  Tuesday, January 8th, 2013