Triangle
Properties
Part A
Table of Contents
SWBAT: Solve Problems involving the Bisectors and Medians of Triangles
DAY 1: (Ch. 5-1/5-3)
Pgs: 1-9
HW: Pgs: #9-11
DAY 2: (Ch. 5-2)
Pgs: 12-16
HW: Pgs: #17-19
SWBAT: Solve Problems involving the Concurrent Lines in Triangles
DAY 3: (5-4)
Pgs: 20-24
HW: Page: 25
SWBAT: Solve Problems involving the Midsegments of Triangles
Day 4 – QUIZ
SWBAT: Review Sections 5.1 thru 5.4
Pgs: 26-30
DAY 5: (5-5)
Pgs: 31-35
HW: Pgs: #36-37
SWBAT: Solve Problems involving Angle Relationships and Inequalities in Triangles.
DAY 8: (Overall Review)
Pgs: 38-43
Day 1 – Bisectors and Medians of Triangles
Definition of Perpendicular Bisector - A line that is perpendicular to and bisects
another segment.
⃡
̅̅̅̅
1
Perpendicular Bisector Theorem
• If a point is on the perpendicular bisector of a segment, then it is
equidistant from the endpoints of the segment.
Given: ⃡
then _____
_____ and _____
̅̅̅̅
_____
The converse is also true:
Example 1:
Find AB.
Example 2:
Find WZ.
2
You Try It!
3
Ex 1: Find AB if DB = 14.1
Ex 2: Find AD if AB = 40.8
4
Using the CENTROID THEOREM
Ex 3: K is the centroid of ABC. Find AH if KH = 6
Ex 4: L is the centroid of DEF.
Find DL if DI = 21
Ex 5: You Try It!
5
Ex 6: ALGEBRA
Ex 7: You Try It!
6
CENTROID AND COORDINATE GEOMETRY
Ex 8: Find the centroid of ∆ABC.
Ex 9: You Try It!
Find the coordinates of the centroid of the triangle below.
Challenge
7
SUMMARY
8
Exit Ticket
Day 1 – HW
9
10
Equation of the Perpendicular Bisector
11
Day 2 – Concurrent Bisectors of Triangles
Warm - Up
Write the equation of the perpendicular bisector of the segments below with the given points.
X (7, 5) Y (-1, -1)
12
Regents Practice
Algebra Related Question
13
Regents Practice
Algebra Related Question
14
An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.
Every triangle has three altitudes. An altitude can be inside, outside, or on the triangle.
Algebra Related Question
Where is the orthocenter located for various types of triangles?
a. For an acute triangle?
b. For a right triangle?
c. For an obtuse triangle?
____________
_____ ___
________
Regents Related Question
15
Challenge
SUMMARY
16
Day 2 – HW
Special Segments in Triangles
____________
__________________________________________
____________
7)
8)
17
Points of Concurrency
18
19
Day 3 – Midsegments of Triangles
Warm - Up
20
21
9.
10.
11.
12
22
Practice
Find the mAMN.
4. Find the value of n.
23
SUMMARY
Challenge:
Exit Ticket
24
Day 3 - Homework
11. Find the value of n.
12. Find the value of n.
25
Day 4 – Review: Sections 5-1 to 5-4
Warm – Up: Complete the table below.
1) The incenter of a triangle is the intersection of the ________________.
2)
3) The centroid of a triangle is the intersection of the ________________.
26
4) The orthocenter of a triangle is the intersection of the ________________.
5) The incenter and centoid of a triangle are always ________________ a triangle.
6. Match the pictures with the appropriate line segments.
Perpendicular Bisectors
Angle Bisectors
Altitudes
a.
b.
c.
Median
d.
7. Match the pictures with the appropriate points of concurrency.
Circumcenter
Incenter
Centroid
a.
b.
c.
Orthocenter
d.
8.
27
9.
10. Find
11.
12. Give the coordinates of the centroid of a triangle with the given vertices:
M (–1, –2), N (3, –3), and P (1, -1)
Centroid _____________
13.
28
14. Use the diagram below to find FG.
15. Write an equation of the perpendicular bisector of the segment with endpoints P(3, 1) and Q(5, 5).
16.
17.
29
30
Day 5 – Inequalities in Triangles
Warm – Up
Objective 1: Angle – Side – Relationships in Triangles
Example 1:
Write the angles in order from smallest to largest.
Example 2:
Write the sides in order from shortest to longest.
31
You Try It!
Example 3:
Example 4:
Example 5: Find the value of x and list the sides of ABC in order from shortest to longest if the
angles have the indicated measures.
32
Objective 2: Triangle Inequality Theorem
Example 6:
You Try It!
Example 7:
Example 8:
33
Example 9:
The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of possible lengths for the third
side.
You Try It!
The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of possible lengths for the
third side.
You Try It!
CHALLENGE
34
SUMMARY
Exit Ticket
35
Day 5 – HW
36
37
Day 6 – Overall Review
38
39
15. Write the equation of the line containing the perpendicular bisector to EF given E (4, 8) and F (-2, 6).
Write you answer in point-slope and slope-intercept form.
40
18.
19.
20.
41
REVIEW OF POINTS OF CONCURRENCY
42
43