Table of Contents Date: Topic: Description: Page:.

Slides:

Advertisements

Similar presentations

Brain Strain Find the value of x. x x x xx Special Segments in Triangles.

Advertisements

Date: Sec 5-4 Concept: Medians and Altitudes of a Triangle

1 Relationships in Triangles Bisectors, Medians, and Altitudes Section 6.1 – 6.3 Students Should Begin Taking Notes At Screen 4!!

Lesson 5-1 Bisectors, Medians, and Altitudes. Ohio Content Standards:

 Definition:  A line that passes through the midpoint of the side of a triangle and is perpendicular to that side.

5-3 Concurrent Lines, Medians, Altitudes

Concurrent Lines Geometry Mrs. King Unit 4, Day 7.

Medians, Altitudes and Concurrent Lines Section 5-3.

Properties of Triangles

5.3 - Concurrent Lines, Medians, and Altitudes

Thinking Page… Directions: Take out your math encyclopedia and review your notes for this unit. Write two paragraphs using complete sentences and correct.

 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.

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.

Chapter 5.3 Concurrent Lines, Medians, and Altitudes

Objectives To define, draw, and list characteristics of: Midsegments

5.3: Concurrent Lines, Medians and Altitudes Objectives: To identify properties of perpendicular bisectors and angle bisectors To identify properties of.

Geometry Grab your clicker and get ready for the warm-up.

Median and Altitude of a Triangle Sec 5.3

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.

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.

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.

Points of Concurrency The point where three or more lines intersect.

Special Segments of Triangles Advanced Geometry Triangle Congruence Lesson 4.

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 SECTIONS 5.2, 5.3, 5.4.

Points of Concurrency MM1G3e Students will be able to find and use points of concurrency in triangles.

5.3 Concurrent Lines, Medians, and Altitudes Stand 0_ Can you figure out the puzzle below??? No one understands!

The 5 special segments of a triangle …again Perpendicular bisector Angle bisector Median Altitude Perpendicular and thru a midpoint of a side Bisects an.

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

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.

Special lines in Triangles and their points of concurrency Perpendicular bisector of a triangle: is perpendicular to and intersects the side of a triangle.

Unit Essential Question: How do you use the properties of triangles to classify and draw conclusions?

Bisectors, Medians, and Altitudes

Section 5 – 3 Concurrent Lines, Medians, and Altitudes

Chapter 5 Lesson 3 Objective: To identify properties of medians and altitudes of a triangle.

Medians and Altitudes of Triangles

Medians, Altitudes and Perpendicular Bisectors

Relationships in Triangles

Special Segments in a Triangle

Triangle Centers Points of Concurrency

Transformations Transformation is an operation that maps the original geometric figure, the pre-image , onto a new figure called the image. A transformation.

You need your journal The next section in your journal is called special segments in triangles You have a short quiz.

Medians and Altitudes of a Triangle

Vocabulary and Examples

Special Segments in Triangles

Lines, Angles and Triangles

If we use this next year and want to be brief on the concurrency points, it would be better to make a table listing the types of segments and the name.

Lines Associated with Triangles 4-3D

Bisectors, Medians and Altitudes

Relationships in Triangles

5-1 HW ANSWERS Pg. 327 # Even 18. CF 10. PS = DA & DB

Lesson 5-3: Bisectors in Triangles

Centroid Theorem By Mario rodriguez.

Section 6.6 Concurrence of Lines

5.3 Concurrent Lines, Medians, and Altitudes

5.3 Concurrent Lines, Medians, and Altitudes

Perpendiculars and Bisectors

Bisectors, Medians, and Altitudes

Medians and Altitudes of Triangles

Altitude, perpendicular bisector, both, or neither?

5-2 Medians and Altitudes of Triangles

concurrency that we will be discussing today.

Presentation transcript:

Table of Contents Date: Topic: Description: Page:

5.2 Notes: Medians and Altitudes of Triangle

The length of this snickers bar is 18cm. What is 2/3 the length The length of this snickers bar is 18cm. What is 2/3 the length? What is 1/3 of the length of the snickers bar? 18cm.

Vocabulary Median: A segment with endpoints being a vertex of the triangle and the midpoint of the opposite side. Centroid: The point of concurrency of the medians of the triangle Centroid Theorem: The centroid that is 2/3 of the distance from each vertex and 1/3 the distance from each side.

Example 1: In ΔXYZ, P is the centroid and YV = 12. Find YP and PV. Given the information about triangle XYZ, how can I mark up the triangle if knowing P is the centroid?

Example 2: In ΔABC, CG = 4. Find GE. Given the picture of the triangle, what is G in my picture?

Vocabulary Altitude: A segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. Orthocenter: The lines containing the altitudes of a triangle are concurrent, intersecting at a point.

Perpendicular Bisector Point of Concurrency : Special Property:

Angle Bisector Point of Concurrency : Special Property:

Median Point of Concurrency : Special Property:

Altitude Point of Concurrency : Special Property:

Summary! In ∆𝑃𝑄𝑅, NQ = 6, RK = 3, and PK = 4. Find each measure using the figure below. KM 2) KQ LK 4) LR NK 6) PM

Summary! Draw an altitude from point B to 𝐴𝐶 in triangle ABC. Make all necessary markings.

Summary! For numbers 8 - 11, give the name of the point of concurrency for each of the following. 8. Angle Bisectors of a Triangle 9. Medians of a Triangle 10. Altitudes of a Triangle 11. Perpendicular Bisectors of a Triangle

Summary! For numbers 12 – 13, complete each of the following statements. 12. The incenter of a triangle is equidistant from the _______________ of the triangle. 13. The circumcenter of a triangle is equidistant from the _________________ of the triangle.