Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.
-
Upload
louisa-mitchell -
Category
Documents
-
view
219 -
download
0
Transcript of Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.
![Page 1: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/1.jpg)
Parallel Lines and the Triangle Angle-Sum Theorem
Geometry
Mrs. King
Unit 3, Lesson 3
![Page 2: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/2.jpg)
Theorem 2-1Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180.
![Page 3: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/3.jpg)
Video: Sum of the Angles of a Triangle
![Page 4: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/4.jpg)
Find the measure of the missing angle
http://www.mathsisfun.com/geometry/images/triangle-missing-angle.gifhttp://maths.fallibroome.cheshire.sch.uk/triangle.jpg
http://www.gizapyramid.com/basic_triangle_w-angles.gif
x
x
![Page 5: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/5.jpg)
Practice
• Find all Variables:
![Page 6: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/6.jpg)
Practice
• Find all Variables:
![Page 7: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/7.jpg)
Practice
• Find all variables
![Page 8: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/8.jpg)
Definition
Exterior Angle: an angle formed by the side of a polygon and an extension of a side.
http://www.freemathhelp.com/images/lessons/exterior1.gif
![Page 9: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/9.jpg)
Definition
Remote Interior Angle: the two nonadjacent interior angles to an exterior angle.
http://www.freemathhelp.com/images/lessons/exterior1.gif
![Page 10: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/10.jpg)
Theorem 2-2Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
![Page 11: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/11.jpg)
Find the measure of the missing angle
http://www.kwiznet.com/px/homes/i/grade8/math/Grade_VIII_Triangles_And_Polygons_PB2_QuestionNo.5.gif
![Page 12: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/12.jpg)
Find the measure of the missing angle
http://www.freemathhelp.com/images/lessons/exterior2.gif
![Page 13: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/13.jpg)
Definition
Corollary: a statement that follows directly from a theorem.
![Page 14: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/14.jpg)
Corollary to Theorem 2-2
The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.
![Page 15: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/15.jpg)
Types of Triangles (by sides)
• Equilateral
• Isosceles
• Scalene
![Page 16: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/16.jpg)
Equilateral Triangles
• Definition:– A triangle with three
congruent sides.
• Example:
![Page 17: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/17.jpg)
Isosceles Triangles
• Definition:– A triangle with two
congruent sides.
• Example:
![Page 18: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/18.jpg)
Scalene Triangles
• Definition:– A triangle with no
congruent sides.
• Example:
![Page 19: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/19.jpg)
Types of Triangles (by angle)
• Equiangular
• Acute
• Right
• Obtuse
![Page 20: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/20.jpg)
Equiangular Triangles
• Definition:– A triangle with three
congruent angles.
• Example:
![Page 21: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/21.jpg)
Acute Triangles
• Definition:– A triangle whose
angles are all acute.
• Example:
![Page 22: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/22.jpg)
Right Triangles
• Definition:– A triangle with one
right angle.
• Example:
![Page 23: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/23.jpg)
Obtuse Triangles
• Definition:– A triangle with one
obtuse angle.
• Example:
![Page 24: Parallel Lines and the Triangle Angle-Sum Theorem Geometry Mrs. King Unit 3, Lesson 3.](https://reader030.fdocuments.us/reader030/viewer/2022032702/56649cf65503460f949c59af/html5/thumbnails/24.jpg)
The three sides of the triangle have three different lengths, so the triangle is scalene.One angle has a measure greater than 90, so the triangle is obtuse.
The triangle is an obtuse scalene triangle.
Classify the triangle by its sides and its angles.