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Section 1.5 Special Points in Triangles
CONCURRENT The point where 3 or more lines intersect
TRIANGLES & CIRCLES What are some things you already know about triangles or circles?
How many sides does a triangle have? What kinds of triangles are there? PREVIOUS FACTS…
WHAT IS A PERPENDICULAR BISECTOR??
PERPENDICULAR BISECTOR Forms right angles. Splits the segment in half
PERPENDICULAR BISECTORS & TRIANGLES Now let’s combine perpendicular bisectors and triangles.
BEGIN BY… Finding the perpendicular bisector of each side of the triangle.
WHAT CAN WE CONCLUDE? What happens when these 3 lines intersect? What is formed?
Perpendicular Bisectors The perpendicular bisectors of a triangle ____________ at a single __________.
CIRCUMCENTER The intersection point of the perpendicular bisectors of a triangle
Circumcenter of an Obtuse Triangle
WHAT IS A ANGLE BISECTOR??
Splits the angle in half ANGLE BISECTOR
ANGLE BISECTORS & TRIANGLES Now let’s combine angle bisectors and triangles.
BEGIN BY… Finding the angle bisector of each angle of the triangle.
WHAT CAN WE CONCLUDE? What happens when these 3 lines intersect? What is formed?
Angle Bisector The angle bisectors of a triangle __________ at a single _________.
INCENTER The intersection point of the angle bisectors of a triangle
INSCRIBED & CIRCUMSCRIBED CIRCLES
INSCRIBED Inside the triangle Just touches the three sides of the triangle.
Another definition of Incenter: The center of an inscribed circle INCENTER
CIRCUMSCRIBED Outside the triangle Contains all 3 vertices
The center of a circumscribed circle CIRCUMCENTER
A couple of other definitions you need to know
Altitude A perpendicular line segment from a vertex of a triangle to the line containing the opposite side. How many altitudes can a triangle have?
Median A line segment from a vertex to the midpoint of the opposite side.
Centroid The point where the 3 medians meet
Special lines in Triangles and their points of concurrency Perpendicular bisector of a triangle: is perpendicular to and intersects the side of a triangle.
5-3 Concurrent Lines, Medians, Altitudes When two lines intersect at one point, we say that the lines are intersecting. The point at which they intersect.
Chapter 5.3 Concurrent Lines, Medians, and Altitudes.
5.3 - Concurrent Lines, Medians, and Altitudes. When three or more lines intersect in one point, they are concurrent. The point at which they intersect.
Concurrent Lines Geometry Mrs. King Unit 4, Day 7.
Geometry B POINTS OF CONCURRENCY. The intersection of the perpendicular bisectors. CIRCUMCENTER.
5.3: Concurrent Lines, Medians and Altitudes Objectives: Students will be able to… Identify properties of perpendicular bisectors and angle bisectors Identify.
1 Objectives To define, draw, and list characteristics of: –Midsegments –Altitudes –Perpendicular Bisectors –Medians.
Points of Concurrency The point where three or more lines intersect.
Top second box. MEDIANS! To the left Point of Concurrency Location It will always be located inside the triangle, because you draw a median from the.
Geometry Sections 5.2 & 5.3 Points of Concurrency.
3.6—Bisectors of a Triangle Warm Up 1. Draw a triangle and construct the bisector of one angle. 2. JK is perpendicular to ML at its midpoint K. List the.
Points of Concurrency Triangles. Point of Concurrency- ________ or more lines (rays or segments) that intersect are called _____________. The point where.
5-3 Bisectors in Triangles. Concurrent: When three or more lines intersect at one point Point of Concurrency: The point at which the points intersect.
Chapter 5.2 & 5.3 BISECTORS, MEDIANS AND ALTITUDES.
Medians, and Altitudes. When three or more lines intersect in one point, they are concurrent. The point at which they intersect is the point of concurrency.
Section 5-2 Bisectors of a Triangle. Perpendicular bisector of a triangle A line, ray, or segment that is perpendicular to a side of the triangle at the.
5-3 Points of Concurrency Objective: To identify properties of perpendicular bisectors and angle bisectors.
Please get a warm up and begin working. Special Parts of Triangles Please get: ♥ Cheat for special segments and lines in triangles ♥ Scissors ♥ Glue or.
Homework Quiz. Warmup Need Graph Paper/Compass 5.3 Concurrent Lines, Medians, and Altitudes.
5.3: Concurrent Lines, Medians and Altitudes Objectives: To identify properties of perpendicular bisectors and angle bisectors To identify properties of.
Median and Altitude of a Triangle Sec 5.3 Goal: To use properties of the medians of a triangle. To use properties of the altitudes of a triangle.
Points of Concurrency Where multiple lines, segments rays intersect, have specific properties.
Section 5-3 Concurrent Lines, Medians, and Altitudes.
Proving Centers of Triangles Adapted from Walch Education.
Geometry Foldable Use this foldable to go with the Euler Points learned in Chapter 5 –Circumcenter –Incenter –Centroid –Orthocenter Make your foldable.
Bisectors in Triangles Chapter 5 Section 3. Objective Students will identify properties of perpendicular bisectors and angle bisectors.
5.2 Bisectors of Triangles5.2 Bisectors of Triangles Use the properties of perpendicular bisectors of a triangle Use the properties of angle bisectors.
SPECIAL SEGMENTS OF TRIANGLES SECTIONS 5.2, 5.3, 5.4.
Constructions Involving Circles Section 7.4. Definitions Concurrent: When three or more lines meet at a single point Circumcenter of a Triangle: The point.
GOALS: 1. To know the definitions of incenter, circumcenter, and centroid. 2. To identify the incenter, circumcenter, and centroid given a diagram. 3.
Geometry Unit 5: Triangle Parts. CONCURRENT: Concurrent: When three or more lines intersect at the same point, P P.
4.5 isosceles and Equilateral Triangles -Theorem 4.3: Isosceles Triangle theorem says if 2 sides of a triangle are congruent, then the angles opposite.
POINTS OF CONCURRENCY In this lesson we will define what a point of concurrency is. Then we will look at 4 points of concurrency in triangles. As you go.
Special Parts of Triangles Day 1 Please get: Activity 1 off the back table 8 pieces of patty paper Compass Protractor Scissors Glue stick Pencil.
Drill Write your homework in your planner Take out your homework Solve for x:
Lesson 12 – Points of Concurrency II. Page 53 The point of concurrency of the medians is known as the centroid which is the center of gravity.
Chapter 5: Relationships within Triangles 5.3 Concurrent Lines, Medians, and Altitudes.
By: Isaac Fernando and Kevin Chung. Do Now: what is a point of concurrency?
Chapter 10 Section 3 Concurrent Lines. If the lines are Concurrent then they all intersect at the same point. The point of intersection is called the.
Chapters 3.7 – 3.8 “Nothing in life is to be feared, it is only to be understood.” Marie Cure.
Medians, altitudes, and perpendicular bisectors May 1, 2008.
MODULE IV VOCABULARY PART II. MODULE IV In continuing our discussion of triangles, it is important that we discuss concurrent lines and points of concurrence.
Definition: A line that passes through the midpoint of the side of a triangle and is perpendicular to that side.
5.3 Notes Bisectors in Triangles. Concurrent When three or more lines intersect at one point, they are concurrent The point at which they intersect is.
JRLeon Discovering Geometry Chapter 3.8 HGSH Pg. 185 In the previous lesson you discovered that the three angle bisectors are concurrent, the three perpendicular.
Warm up 1.If you drew an angle on a piece of patty paper and were told to fold an angle bisector, how would you do it? 2.If you drew a segment on a piece.
5-2 Perpendicular and Angle Bisectors. Perpendicular Bisectors A point is equidistant from two objects if it is the same distance from each. A perpendicular.
5.2 Bisectors of a Triangle Concurrent lines CircumcenterIncenter.
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