Slide 1

Slide 2

Using Properties of Angle Bisectors Remember? 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.

Slide 3

1.Rotation 2.Reflection 10 minutes

Slide 4

Geometry IB HR Date: 2/13/2013 ID Check 2 nd,4 th, 6 th, 7 th 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 2 nd 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.

Slide 5

Geometry 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 entry Bronson 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 3 rd side to the nearest foot. Find the measure of each angle? HW Requests: None HW: pg 327 #9-20 Read Section 5.1 Announcements: Construction WS Due Friday 1/31 Life Is Just A Minute Life 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

Slide 6

Perpendicular 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 triangle http://www.youtube.com/watch?v=lcBUOP5nk3U

Slide 7

Pg 322 http://youtu.be/KXZ6w91DioU

Slide 8

Ex. 1 Using Perpendicular Bisectors In the diagram MN is the perpendicular bisector of ST. a.What segment lengths in the diagram are equal? b.Explain why Q is on MN. c. If TM = 2x+3 and SM = 4x-7. What is the length of TM and SM?

Slide 9

Ex. 1 Using Perpendicular Bisectors a.What 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. b.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.

Slide 10

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 OA 1 = OA 2 = OA 3.

Slide 11

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.

Slide 12

Exit Ticket: pg 327 #1-4

Slide 13

Geometry 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 clips Protractor, Ruler, 2 Pencils HW Requests: pg 327 #9-20 HW: pg 328 #21-29 odds, 32-35, 37, 41, 42, 45 Read Section 5.2 Announcements: Credit Recovery Registration Construction WS Due Friday 1/31 Life Is Just A Minute Life 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

Slide 14

Pg 325

Slide 15

Slide 16

Name: _____________________________________Date:________________Per:_____________ Constructions pg 321 Materials: Triangle paper Compass 4 paper clips Protractor Straightedge 2 Pencils

Slide 17

Slide 18

Slide 19

Ex. 3: Using Angle Bisectors Roof 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?

Slide 20

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.

Slide 21

Slide 22

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.

Slide 23

Theorem 5.2: Converse of the Perpendicular Bisector Theorem If 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.

Slide 24

What is the best way to track the constellations? How does GPS work?

Slide 25

Placing Triangles on coordinate plane Key Concept pg 301 Step 1: Use the origin as a vertex or center of the triangle Step 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.

Slide 26

Slide 27

Slide 28

Geometry HR Date: 2/8/2013 ID Check Objective: Identify reflections, translations, an rotations and verify congruence after a congruence transformation. Bell Ringer: See overhead HW Requests: pg 297 #7-23 odds Parking Lot: Perfect Square Trinomials, OEA #33 In 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.

Slide 29

Slide 30

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. 4.6 HW Requests: pg 287 #9-21 odds, 29-32, 38, OEA #33 Parking Lot: Perfect Square Trinomials In class: Take Cornell Notes Pg 297 #1-6, pg 299 #24-26, 32 HW: pg 297 #7-23 odds Exit Ticket: pg 299 #24-26, 32 Announcements: Quiz Section 4.6-4.8 Monday If at first you dont succeed, try and try again.

Slide 31

Pg 294

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

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 Notes HW: 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 Problems pg 287 #1-7

Slide 46

Slide 47

Properties of Isosceles Triangles Vertex Angle The angle formed by the congruent sides. Base Angle Two angles formed by the base and one of the congruent sides.

Slide 48

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.

Slide 49

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.

Slide 50

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.

Slide 51

Slide 52