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.