Slide 1
Using Properties of Angle BisectorsRemember?The distance from a
point to a line is defined as the length of the perpendicular
segment from the point to the line. For instance, in the diagram
shown, the distance between the point Q and the line m is QP.
RotationReflection10 minutesGeometry IB HR Date: 2/13/2013 ID
Check 2nd,4th, 6th, 7th Objective: SWBAT identify and use
perpendicular and angle bisectors in triangles.
Bell Ringer: 5 minute check 4.6/4.7 10 minutes
HW Requests: pg 304 #7-18/ Quadratics WS 2nd
HW: pg Pg 327 #9-14, 21-26, 41, 42
Announcements:Quiz Section 4.6-4.8 Thursday
If at first you dont succeed, try and try again.3Geometry IB_HR
Date: 1/29/2014 ID Check Objective: SWBAT identify and use
perpendicular and angle bisectors in triangles.Bell Ringer: Turn In
Take Home Test Due upon entryBronson is creating a rt. triangular
flower bed. If 2 sides of the flower bed are 7 ft long each, what
is the length of the 3rd side to the nearest foot. Find the measure
of each angle?HW Requests: None
HW: pg 327 #9-20Read Section 5.1
Announcements: Construction WS Due Friday 1/31Life Is Just A
MinuteLife is just a minuteonly sixty seconds in it.Forced upon
youcan't refuse it.Didn't seek itdidn't choose it.But it's up to
you to use it.You must suffer if you lose it.Give an account if you
abuse it.Just a tiny, little minute,But eternity is in it!
By Dr. Benjamin Elijah Mays, Past President of Morehouse
College
4Perpendicular Bisector A segment, ray, line, or plane that is
perpendicular to a segment at its midpoint is called a
perpendicular bisector.
Perpendicular Bisectors in a
trianglehttp://www.youtube.com/watch?v=lcBUOP5nk3U
Pg 322http://youtu.be/KXZ6w91DioU Ex. 1 Using Perpendicular
BisectorsIn the diagram MN is the perpendicular bisector of ST.
What segment lengths in the diagram are equal?Explain why Q is on
MN.c. If TM = 2x+3 and SM = 4x-7. What is the length of TM and
SM?
Ex. 1 Using Perpendicular BisectorsWhat segment lengths in the
diagram are equal? Solution: MN bisects ST, so NS = NT. Because M
is on the perpendicular bisector of ST, MS = MT. (By Theorem 5.1).
The diagram shows that QS = QT = 12.
Explain why Q is on MN.Solution: QS = QT, so Q is equidistant
from S and T. By Theorem 5.2, Q is on the perpendicular bisector of
ST, which is MN.Perpendicular Bisector
Line, segment or ray that passes through the midpoint of the
side and is perpendicular to that side.
Circumcenter intersection of the 3 bisectors. The circumcenter
is equidistant from the vertices. If O is the circumcenter OA1 =
OA2 = OA3.
http://www.mathopenref.com/trianglecircumcenter.html Concurrent
Lines: three or more lines intersect at a common point.Point of
concurrency: point where concurrent lines intersect.
Exit Ticket: pg 327 #1-4Geometry IB_HR Date: 1/30/2014 ID Check
Objective: SWBAT identify and use perpendicular and angle bisectors
in triangles.Bell Ringer: Get Triangle paper, Compass 4 paper
clipsProtractor, Ruler, 2 Pencils HW Requests: pg 327 #9-20
HW: pg 328 #21-29 odds, 32-35, 37, 41, 42, 45Read Section
5.2Announcements: Credit Recovery RegistrationConstruction WS Due
Friday 1/31Life Is Just A MinuteLife is just a minuteonly sixty
seconds in it.Forced upon youcan't refuse it.Didn't seek itdidn't
choose it.But it's up to you to use it.You must suffer if you lose
it.Give an account if you abuse it.Just a tiny, little minute,But
eternity is in it!
By Dr. Benjamin Elijah Mays, Past President of Morehouse
College
12
Pg 325
Name:
_____________________________________Date:________________Per:_____________Constructions
pg 321Materials:Triangle paperCompass 4 paper
clipsProtractorStraightedge2 Pencils
Ex. 3: Using Angle BisectorsRoof Trusses: Some roofs are built
with wooden trusses that are assembled in a factory and shipped to
the building site. In the diagram of the roof trusses shown, you
are given that AB bisects CAD and that ACB and ADB are right
angles. What can you say about BC and BD?
SOLUTION:Because BC and BD meet AC and AD at right angles, they
are perpendicular segments to the sides of CAD. This implies that
their lengths represent distances from the point B to AC and AD.
Because point B is on the bisector of CAD, it is equidistant from
the sides of the angle.So, BC = BD, and you can conclude that BC
BD.
Theorem 5.1 Perpendicular Bisector Theorem If a point is on the
perpendicular bisector of a segment, then it is equidistant from
the endpoints of the segment.
If CP is the perpendicular bisector of AB, then CA = CB.
Theorem 5.2: Converse of the Perpendicular Bisector TheoremIf a
point is equidistant from the endpoints of a segment, then it is on
the perpendicular bisector of the segment.
If DA = DB, then D lies on the perpendicular bisector of AB.
What is the best way to track the constellations?How does GPS
work?
Placing Triangles on coordinate planeKey Concept pg 301Step 1:
Use the origin as a vertex or center of the triangleStep 2: Place
at least one side of a triangle on an axis.Step 3: Keep the
triangle within the first quadrant, if possible.Step 4: Use
coordinates that make computations as simple as possible.
Geometry HR Date: 2/8/2013 ID Check Objective: Identify
reflections, translations, an rotations and verify congruence after
a congruence transformation.
Bell Ringer: See overheadHW Requests: pg 297 #7-23 oddsParking
Lot: Perfect Square Trinomials, OEA #33In class: Graph pg 298
#17-20,HW: Quadratic WS (Half Sheet)
Announcements:Quiz Section 4.6-4.8 Monday
If at first you dont succeed, try and try again.27
Geometry IB-HR Date: 2/7/2013 ID Check Objective: Identify
reflections, translations, an rotations and verify congruence after
a congruence transformation.
Bell Ringer: Go over Red WB Sect. 4.6HW Requests: pg 287 #9-21
odds, 29-32, 38, OEA #33Parking Lot: Perfect Square TrinomialsIn
class: Take Cornell NotesPg 297 #1-6, pg 299 #24-26, 32HW: pg 297
#7-23 odds
Exit Ticket: pg 299 #24-26, 32Announcements:Quiz Section 4.6-4.8
Monday
If at first you dont succeed, try and try again.29
Pg 294
Geometry IB -HR Date: 2/4/2013 ID Check
Objective: Use properties of isosceles and equilateral
triangles.Bell Ringer: Put OEA in Bin - Go over OEA #46.HW
Requests: Pg 291 #52-55
In class: Take Cornell NotesHW: pg 287 #9-21 odds, 29-32, 38,
OEA #33; Read Sect. 4.7
Announcements:Quiz Section 4.6-4.8 Monday If at first you dont
succeed, try and try again.Exit Ticket:Selected Problemspg 287
#1-7
44
Properties of Isosceles Triangles
Vertex AngleThe angle formed by the congruent sides.Base Angle
Two angles formed by the base and one of the congruent sides.Thm.
4.10 -Isosceles Triangle Thm.
Ex: Proof 1
If two sides of a triangle are congruent, then the angles
opposite those sides are congruent.
Thm. 4.11 Converse of Isosceles Triangle Theorem
Ex: Proof
If two angles of a triangle are congruent, then the sides
opposite those angles are congruent.
Equilateral Triangles
Corrollary 4.3 A is equilateral if and only if it is
equiangular.Corrollary 4.4 Each angle of an equilateral measures 60
degrees.