D is the midpoint of AC and E is the midpoint of AB. Find x, the length of segment DE, DC, and AC. X = 4 DE = 6.5 DC = 4 AC = 8 BB.

Slides:



Advertisements
Similar presentations
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.
Advertisements

Section 1.5 Special Points in Triangles
Section 4.7 Medians, Altitudes, and Perpendicular Bisectors
4-7 Median, Altitude, and Perpendicular bisectors.
Medians, Altitudes and Perpendicular Bisectors
Chapter 5 Perpendicular Bisectors. Perpendicular bisector A segment, ray or line that is perpendicular to a segment at its midpoint.
Basic Definitions in Geometry
5.2 Bisectors of a Triangle Concurrent lines CircumcenterIncenter.
GOALS: 1. To know the definitions of incenter, circumcenter, and centroid. 2. To identify the incenter, circumcenter, and centroid given a diagram. 3.
Relationships within triangles
Points of Concurrency in Triangles Keystone Geometry
5-3 Concurrent Lines, Medians, Altitudes
5.2 Bisectors of Triangles5.2 Bisectors of Triangles  Use the properties of perpendicular bisectors of a triangle  Use the properties of angle bisectors.
Medians, Altitudes, and Angle Bisectors Honors Geometry Mr. Manker.
Chapter 5 Perpendicular Bisectors. Perpendicular bisector A segment, ray or line that is perpendicular to a segment at its midpoint.
Concurrent Lines Geometry Mrs. King Unit 4, Day 7.
Triangle – a three sided polygon (straight sides; closed) A B C 3 sides: 3 angles: 3 vertices: A, B, C.
5-3 Points of Concurrency Objective: To identify properties of perpendicular bisectors and angle bisectors.
5.3 - Concurrent Lines, Medians, and Altitudes
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.
Chapter 5.3 Concurrent Lines, Medians, and Altitudes
Bisectors of a Triangle
Objectives To define, draw, and list characteristics of: Midsegments
By: Isaac Fernando and Kevin Chung.  Do Now: what is a point of concurrency?
5.3: Concurrent Lines, Medians and Altitudes Objectives: To identify properties of perpendicular bisectors and angle bisectors To identify properties of.
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.
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.
Medians, altitudes, and perpendicular bisectors May 1, 2008.
Median and Altitude of a Triangle Sec 5.3
MEDIANS, ALTITUDES, AND PERPENDICULAR BISECTORS October 13, 2009.
Points of Concurrency Triangles.
Special Segments of Triangles
Lesson 12 – Points of Concurrency II
5.4 Medians and Altitudes A median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side. –A triangle’s three medians.
5-3 Bisectors in Triangles
Vocabulary Unit 4 & 5. Equilateral/Equiangular Triangle A triangle with 3 congruent sides and 3 congruent angles.
Geometry B POINTS OF CONCURRENCY. The intersection of the perpendicular bisectors. CIRCUMCENTER.
Geometry Lesson 5 – 1 Bisectors of Triangles Objective: Identify and use perpendicular bisectors in triangles. Identify and use angle bisectors in triangles.
Perpendicular Bisectors of a Triangle Geometry. Equidistant A point is equidistant from two points if its distance from each point is the same.
Points of Concurrency The point where three or more lines intersect.
Lesson 5-2 Use perpendicular bisectors
5.3: Concurrent Lines, Medians and Altitudes Objectives: Students will be able to… Identify properties of perpendicular bisectors and angle bisectors Identify.
Perpendicular and Angle Bisectors Perpendicular Bisector – A line, segment, or ray that passes through the midpoint of a side of a triangle and is perpendicular.
SPECIAL SEGMENTS OF TRIANGLES SECTIONS 5.2, 5.3, 5.4.
Chapter 5.2 & 5.3 BISECTORS, MEDIANS AND ALTITUDES.
5.2 Bisectors of a Triangle Advanced Geometry. PERPENDICULAR BISECTOR OF A TRIANGLE A perpendicular bisector of a triangle is a line (ray or segment)
How do we analyze the special segments that exist inside triangles? Agenda: Warmup Go over homework Segments inside triangles notes/practice QUIZ Thursday.
Geometry Sections 5.2 & 5.3 Points of Concurrency.
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.
Special lines in Triangles and their points of concurrency Perpendicular bisector of a triangle: is perpendicular to and intersects the side of a triangle.
Use Medians and Altitudes
Medians and Altitudes of Triangles
5.4: Use Medians and Altitudes
Bisectors, Medians, and Altitudes
Section 5. 3: Use Angle Bisectors in Triangles Section 5
Perpendicular Bisectors
Triangle Centers Points of Concurrency
Vocabulary and Examples
Special Segments in Triangles
Bisectors, Medians and Altitudes
Section 5.1.
4-7 Medians, Altitudes, and Perpendicular Bisectors
Medians Picture: Both sides are congruent Median vertex to midpoint.
Medians, Altitudes, & Perpendicular Bisectors
Lesson 5-3: Bisectors in Triangles
Centroid Theorem By Mario rodriguez.
5.3 Concurrent Lines, Medians, and Altitudes
4-7 Medians, Altitudes, and Perpendicular Bisectors
Medians and Altitudes.
concurrency that we will be discussing today.
Presentation transcript:

D is the midpoint of AC and E is the midpoint of AB. Find x, the length of segment DE, DC, and AC. X = 4 DE = 6.5 DC = 4 AC = 8 BB

Cornell Notes Concurrent lines Collinear Three or more lines that meet or intersect at one point are concurrent lines Three or more points that are on the same line are collinear points

Acute Triangle Obtuse Triangle Right triangle A triangle with three acute angle (less than 90 degrees) A triangle with one obtuse angle (more than 90 degrees) A triangle with one right angle ( 90 degree angle)

Turn on your calculator. Go to house, 7 (my documents). Click on You should see a triangle with three perpendicular bisectors. Perpendicular bisector Circumcenter Point where perpendicular bisectors meet A line that is perpendicular to a segment at its midpoint

Move around vertex B to form each of the following triangles: acute, obtuse, and right. Draw sketches in your notes for each triangle. Acute triangle: Obtuse triangle: Right triangle: Where are the perpendicular bisectors concurrent? Inside the triangle Outside the triangle On the triangle

Press Ctrl over to move to tab 1.2. It should say Angle bisector. Move around vertex B to form each of the following triangles: acute, obtuse, and right. Draw sketches in your notes for each triangle. Angle bisector A ray that divides an angle into 2 congruent angles. What do you notice about the incenter in each of the triangles? Where are the angle bisectors concurrent? IncenterPoint where angle bisectors meet The angle bisectors are always concurrent inside the triangle

Pg. 63 #7 (at least 3 different triangle) and 8 Pg. 64 # 4 Median: a segment from a vertex to the midpoint of the opposite side