Using properties of Midsegments Suppose you are given only the three midpoints of the sides of a triangle. Is it possible to draw the original triangle?

Slides:

Advertisements

Similar presentations

Bisectors in Triangles Academic Geometry. Perpendicular Bisectors and Angle Bisectors In the diagram below CD is the perpendicular bisector of AB. CD.

Advertisements

Chapter 5 Properties of Triangles Perpendicular and Angle Bisectors Sec 5.1 Goal: To use properties of perpendicular bisectors and angle bisectors.

4-7 Median, Altitude, and Perpendicular bisectors.

Medians, Altitudes and Perpendicular Bisectors

5.1: Perpendicular Bisectors

Chapter 5 Perpendicular Bisectors. Perpendicular bisector A segment, ray or line that is perpendicular to a segment at its midpoint.

Geometry (Holt 3-4)K.Santos. Perpendicular Bisector Perpendicular bisector of a segment is a line perpendicular to a segment at the segment’s midpoint.

5-2 Perpendicular and Angle Bisectors Learning Goals 1. To use properties of perpendicular bisectors and angle bisectors.

Geometry Chapter 5 Benedict. Vocabulary Perpendicular Bisector- Segment, ray, line or plane that is perpendicular to a segment at its midpoint. Equidistant-

Chapter 5. Vocab Review  Intersect  Midpoint  Angle Bisector  Perpendicular Bisector  Construction of a Perpendicular through a point on a line Construction.

6.1 Perpendicular and Angle Bisectors

Warm- up Type 2 writing and Construction Write your own definition and draw a picture of the following: Angle Bisector Perpendicular Bisector Draw an acute.

5.2 Perpendicular 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.

Proving the Midsegment of a Triangle Adapted from Walch Education.

Chapter 5 Perpendicular Bisectors. Perpendicular bisector A segment, ray or line that is perpendicular to a segment at its midpoint.

5.1 Bisectors, Medians, and Altitudes. Objectives Identify and use ┴ bisectors and  bisectors in ∆s Identify and use medians and altitudes in ∆s.

Perpendicular & Angle Bisectors. Objectives Identify and use ┴ bisectors and  bisectors in ∆s.

5.4 Midsegment Theorem Geometry Ms. Reser.

Distance and Midpoints

Find the missing angle ?0?0. Special Segments in Triangles.

Midsegment Theorem Geometry Mrs. Spitz Fall 2004.

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.

 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.

Introduction Triangles are typically thought of as simplistic shapes constructed of three angles and three segments. As we continue to explore this shape,

CHAPTER 5 Relationships within Triangles By Zachary Chin and Hyunsoo Kim.

Your 1 st Geometry Test A step by step review of each question.

Bisectors of a Triangle

Geometry Review 1 st Quarter Definitions Theorems Parts of Proofs Parts of Proofs.

Chapter 5 More Triangles. Mr. Thompson More Triangles. Mr. Thompson.

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.

Section 5-1 Perpendiculars and Bisectors. Perpendicular bisector A segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

Bisectors in Triangles Section 5-2. Perpendicular Bisector A perpendicular tells us two things – It creates a 90 angle with the segment it intersects.

Chapter 5.2 Bisectors in Triangles Reminder: Bring your textbook for cd version!

Objectives: Students will be able to…

5-4 Midsegment Theorem Identify the Midsegment of a triangle

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.

Geometry Sections 5.1 and 5.2 Midsegment Theorem Use Perpendicular Bisectors.

5.6 Angle Bisectors and Perpendicular Bisectors

Daily Warm-Up Quiz F H, J, and K are midpoints 1. HJ = __ 60 H 65 J FG = __ JK = __ m < HEK = _ E G Reason: _ K 3. Name all 100 parallel segments.

Isosceles Triangles Theorems Theorem 8.12 – If two sides of a triangle are equal in measure, then the angles opposite those sides are equal in measure.

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.

5.2: Bisectors in Triangles Objectives: To use properties of perpendicular and angle bisectors.

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.

Chapter 5, Section 1 Perpendiculars & Bisectors. Perpendicular Bisector A segment, ray, line or plane which is perpendicular to a segment at it’s midpoint.

LESSON 5-2 BISECTORS IN TRIANGLES OBJECTIVE:

5.4 Midsegment Theorem Geometry 2011.

Medians, Altitudes and Perpendicular Bisectors

Chapter 5.1 Segment and Angle Bisectors

Special Segments in a Triangle

Section 5.4 Theorem – MIDSEGMENT THEOREM The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.

Distance and Midpoints

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

Midsegments of Triangles

2.2.4 Use slope criteria for parallel and perpendicular lines to solve problems on the coordinate plane.

4.1 warm-up A triangle is enlarged by a scale factor of 9. If the length of one side of the larger triangle is centimeters, what is the length.

Bisectors, Medians and Altitudes

5.1 Perpendiculars and Bisectors

Triangle Segments.

Lesson 5.3 Lesson 5.3 Midsegment Theorem

Appetizer Draw, label, and cut out a large triangle; it does not matter what type of triangle. Label (on the inside), the vertices A, B, and C. Fold A.

6.1 Perpendicular and Angle Bisectors

Relationships Within Triangles

5.4 Midsegment Theorem.

Module 15: Lesson 5 Angle Bisectors of Triangles

Introduction Triangles are typically thought of as simplistic shapes constructed of three angles and three segments. As we continue to explore this shape,

5.4 Midsegment Theorem.

SPECIAL SEGMENTS.

Presentation transcript:

Using properties of Midsegments Suppose you are given only the three midpoints of the sides of a triangle. Is it possible to draw the original triangle?

2 Guided Practice: The midpoints of a triangle are X (–2, 5), Y (3, 1), and Z (4, 8). Find the coordinates of the vertices of the triangle. 1. Plot the midpoints on a coordinate plane.

3 Guided Practice: continued 2. Connect the midpoints to form the midsegments,, and.

4 Guided Practice: continued 3. Calculate the slope of each midsegment. Calculate the slope of. The slope of is Slope formula Substitute (–2, 5) and (3, 1) for (x 1, y 1 ) and (x 2, y 2 ). Simplify.

5 Guided Practice: continued Calculate the slope of. The slope of is 7. Slope formula Substitute (3, 1) and (4, 8) Simplify.

6 Guided Practice: continued Calculate the slope of. The slope of is Slope formula Substitute (–2, 5) and (4, 8) Simplify.

7 Guided Practice: 4. Draw the lines that contain the midpoints. The endpoints of each midsegment are the midpoints of the larger triangle. Each midsegment is also parallel to the opposite side.

8 Guided Practice: continued The slope of is From point Y, draw a line that has a slope of

9 Guided Practice: continued The slope of is 7 From point X, draw a line that has a slope of 7

10 Guided Practice: continued The slope of is From point Z, draw a line that has a slope of The intersections of the lines form the vertices of the triangle.

Properties of Triangles Perpendicular and Angle Bisectors Objective: To use properties of perpendicular bisectors and angle bisectors

Perpendicular Bisector Perpendicular Bisector – a segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

Equidistant Equidistant from two points means that the distance from each point is the same.

Perpendicular Bisector Theorem Perpendicular Bisector Theorem – If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Converse of the Perpendicular Bisector Theorem 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 a segment.

Example Does D lie on the perpendicular bisector of

Example

Distance from a point to a line The shortest distance from one point to another is a straight line.

Examples Does the information given in the diagram allow you to conclude that C is on the perpendicular bisector of AB?

WARM-UP

Angle Bisector Theorem Angle Bisector Theorem – If a point (D) is on the bisector of an angle, then it is equidistant from the two sides of the angle.

Converse of the Angle Bisector Theorem Converse of the Angle Bisector Theorem – If a point is on the interior of an angle, and is equidistant from the sides of the angle, then it lies on the bisector of the angle.

Examples Does the information given in the diagram allow you to conclude that P is on the angle bisector of angle A?