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Brain Strain Find the value of x. x x x xx
Special Segments in Triangles
Tell whether each red segment is an altitude of the triangle. The altitude is the true height of the triangle.
Tell whether each red segment is an perpendicular bisector of the triangle.
Drill & Practice Indicate which special triangle segment the red line is based on the picture and markings
Points of Concurrency
The intersection of the angle bisectors is called the INCENTER. Equidistant to the sides
The intersection of the altitudes is called the ORTHOCENTER.
The intersection of the medians is called the CENTROID. Vertex to Centroid is Twice as Long as Centroid to Midpoint
The intersection of the perpendicular bisector is called the CIRCUMCENTER. Equidistant to the vertices
Memorize these! MC AO ABI PBCC Medians/Centroid Altitudes/Orthocenter Angle Bisectors/Incenter Perpendicular Bisectors/Circumcenter
Will this work? MC AO ABI PBCC My Cat Ate Our Apples But I Prefer Blue Cheese Crumbles
Special Property of Medians
Theorem Vertex to CENTROID is TWICE as long as CENTROID to MIDPOINT vertex centroid midpoint
A B F X E C D
A B F X E C D
In ABC, AN, BP, and CM are medians. A B M P E C N If EM = 3, find EC. Ex: 1
In ABC, AN, BP, and CM are medians. A B M P E C N If EN = 12, find AN. Ex: 2
In ABC, AN, BP, and CM are medians. A B M P E C N If CM = 3x + 6, and CE = x + 12, what is x? CM = CE + EM Ex: 3
Warm Up 1.Give the restrictions on the third side of the triangle if the first two sides are 18 and Find x and y for both figures. 55°70° x y 100°
Points of Concurrency The point where three or more lines intersect.
Points of Concurrency MM1G3e Students will be able to find and use points of concurrency in triangles.
The intersection of the medians is called the CENTROID. How many medians does a triangle have?
Centers of Triangles or Points of Concurrency Median.
Warm up: Solve for x. Linear Pair 4x + 3 7x + 12 X = 15.
Centers of Triangles or Points of Concurrency
8/9/2015 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? Warm-Up Take out homework p.301 (4-20) even Check your answers.
Points of Concurrency Triangles.
Geometry B POINTS OF CONCURRENCY. The intersection of the perpendicular bisectors. CIRCUMCENTER.
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.
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, and Altitudes Stand 0_ Can you figure out the puzzle below??? No one understands!
5.3: Concurrent Lines, Medians and Altitudes Objectives: Students will be able to… Identify properties of perpendicular bisectors and angle bisectors Identify.
Special Segments of Triangles
Chapter 5.3 Concurrent Lines, Medians, and Altitudes
Median and Altitude of a Triangle Sec 5.3
1 Relationships in Triangles Bisectors, Medians, and Altitudes Section 6.1 – 6.3 Students Should Begin Taking Notes At Screen 4!!
SPECIAL SEGMENTS OF TRIANGLES SECTIONS 5.2, 5.3, 5.4.
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 - Concurrent Lines, Medians, and Altitudes
5-3 Concurrent Lines, Medians, Altitudes
Angle Bisector A segment that cuts an angle in half.
Perpendicular Bisectors ADB C CD is a perpendicular bisector of AB Theorem 5-2: Perpendicular Bisector Theorem: If a point is on a perpendicular bisector.
Definition: A line that passes through the midpoint of the side of a triangle and is perpendicular to that side.
Sec 6.1 Median.
Points of Concurrency Where multiple lines, segments rays intersect, have specific properties.
Medians, Altitudes, and Angle Bisectors Honors Geometry Mr. Manker.
Special Segments of Triangles Advanced Geometry Triangle Congruence Lesson 4.
Geometry Sections 5.2 & 5.3 Points of Concurrency.
5.3: Concurrent Lines, Medians and Altitudes Objectives: To identify properties of perpendicular bisectors and angle bisectors To identify properties of.
Unit Essential Question: How do you use the properties of triangles to classify and draw conclusions?
The 5 special segments of a triangle …again Perpendicular bisector Angle bisector Median Altitude Perpendicular and thru a midpoint of a side Bisects an.
Bisectors of a Triangle
Perpendicular Bisector- a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side Theorem 5.1 Any point.
Concurrent Lines Geometry Mrs. King Unit 4, Day 7.
LESSON FIFTEEN: TRIANGLES IN TRAINING. MORE TRIANGLE PROPERTIES In the last lesson, we discussed perpendicular bisectors and how they intersect to create.
5-2 Median & Altitudes of Triangles
Finding Equations of Lines If you know the slope and one point on a line you can use the point-slope form of a line to find the equation. If you know the.
Properties of Triangles
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.
Geometry Grab your clicker and get ready for the warm-up.
5.2 Bisectors of Triangles5.2 Bisectors of Triangles Use the properties of perpendicular bisectors of a triangle Use the properties of angle bisectors.
Chapter 5, Section 1 Perpendiculars & Bisectors. Perpendicular Bisector A segment, ray, line or plane which is perpendicular to a segment at it’s midpoint.
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.
Day 4 agenda Go over homework- 5 min Warm-up- 10 min 5.3 notes- 55 min Start homework- 20 min The students will practice what they learned in the computer.
By: Isaac Fernando and Kevin Chung. Do Now: what is a point of concurrency?
Medians, Altitudes and Concurrent Lines Section 5-3.
Lesson 12 – Points of Concurrency II
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