lesson: objectives: 4.1 classifying triangles to identify parts of triangles to classify triangles...
TRANSCRIPT
![Page 1: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/1.jpg)
Lesson:
Objectives:
4.1 Classifying Triangles
To IDENTIFY parts of triangles
To CLASSIFY Triangles by their Parts
![Page 2: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/2.jpg)
Geometry 4.1 Some DEFINITIONS
• acute triangle• obtuse triangle
• right triangle
• equiangular triangle• scalene triangle
• isosceles triangle
• equilateral triangle
![Page 3: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/3.jpg)
Geometry 4.1 Some DEFINITIONS
POLYGON –
![Page 4: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/4.jpg)
Geometry 4.1 Some DEFINITIONS
POLYGON –
a closed figure in a Plane
![Page 5: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/5.jpg)
Geometry 4.1 Some DEFINITIONS
POLYGON –
a closed figure in a Plane
made-up of Segments that
![Page 6: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/6.jpg)
Geometry 4.1 Some DEFINITIONS
POLYGON –
a closed figure in a Plane
made-up of Segments that
intersect only at their Endpoints, called VERTICES.
![Page 7: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/7.jpg)
Geometry 4.1 Some DEFINITIONS
POLYGON –
a closed figure in a Plane
made-up of Segments that
intersect only at their Endpoints, called VERTICES.
TRIANGLE –
a three-sided Polygon
consisting of Sides, Vertices, and Angles
![Page 8: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/8.jpg)
Geometry 4.1
![Page 9: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/9.jpg)
Geometry 4.1
![Page 10: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/10.jpg)
Geometry 4.1
![Page 11: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/11.jpg)
Geometry 4.1
![Page 12: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/12.jpg)
Geometry 4.1
![Page 13: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/13.jpg)
Geometry 4.1
Equiangular
![Page 14: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/14.jpg)
Geometry 4.1
Equiangular Parts of a Right Triangle
![Page 15: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/15.jpg)
Geometry 4.1
Classification of Triangles
Angles
Acute 3 Acute Angles
Obtuse 1 Obtuse Angle
Right 1 Right Angle
Equiangular 3 Angles
![Page 16: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/16.jpg)
Geometry 4.1
![Page 17: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/17.jpg)
Geometry 4.1
![Page 18: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/18.jpg)
Geometry 4.1
![Page 19: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/19.jpg)
Geometry 4.1
![Page 20: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/20.jpg)
Geometry 4.1
![Page 21: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/21.jpg)
Geometry 4.1
![Page 22: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/22.jpg)
Geometry 4.1
Classification of Triangles
Angles Sides
Acute 3 Acute Angles Scalene No 2 sides Obtuse 1 Obtuse Angle Isosceles At Least 2 sides
Right 1 Right Angle Equilateral 3 sides Equiangular 3 Angles
![Page 23: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/23.jpg)
Geometry 4.1
COORDINATE GEOMETRY Find the measures of the sides of ΔRTS. Classify the triangle by sides.
![Page 24: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/24.jpg)
Geometry 4.1
You should be able to:
DEFINE a POLYGON
DEFINE a TRIANGLE
CLASSIFY a Triangle by Type of ANGLES
CLASSIFY a Triangle by Type of SIDES
NAME the Parts of a RIGHT Triangle
![Page 25: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/25.jpg)
Lesson:
Pages:
Objectives:
4.2 Measuring Angles in Triangles
189 – 192
To APPLY the ANGLE SUM Theorem
To APPLY the EXTERIOR ANGLE Theorem
![Page 26: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/26.jpg)
GEOMETRY 4.2
Slide 1 of 150
![Page 27: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/27.jpg)
GEOMETRY 4.2
![Page 28: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/28.jpg)
GEOMETRY 4.2
![Page 29: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/29.jpg)
GEOMETRY 4.2
![Page 30: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/30.jpg)
GEOMETRY 4.2
180 Theorem –
The SUM of the measures of the angles of a Triangle is 180.
![Page 31: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/31.jpg)
GEOMETRY 4.2
180 Theorem –
The SUM of the measures of the angles of a Triangle is 180.
PROVE It!
![Page 32: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/32.jpg)
GEOMETRY 4.2
![Page 33: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/33.jpg)
GEOMETRY 4.2
![Page 34: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/34.jpg)
GEOMETRY 4.2
THIRD ANGLE Theorem –
If TWO Angles of one Triangle are CONGRUENT to
TWO Angles of a second triangle,
then the THIRD angles of the triangles
ARE CONGRUENT.
![Page 35: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/35.jpg)
GEOMETRY 4.2
THIRD ANGLE Theorem –
If TWO Angles of one Triangle are CONGRUENT to
TWO Angles of a second triangle,
then the THIRD angles of the triangles
ARE CONGRUENT.
![Page 36: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/36.jpg)
GEOMETRY 4.2
THIRD ANGLE Theorem –
If TWO Angles of one Triangle are CONGRUENT to
TWO Angles of a second triangle,
then the THIRD angles of the triangles
ARE CONTRUENT.
PROVE It.
![Page 37: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/37.jpg)
GEOMETRY 4.2
Definition: EXTERIOR ANGLE
An Exterior Angle is formed by one side of a triangle and the extension of another side.
![Page 38: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/38.jpg)
GEOMETRY 4.2
Definition: EXTERIOR ANGLE
An Exterior Angle is formed by one side of a triangle and the extension of another side.
Definition: REMOTE INTERIOR ANGLES
The Interior Angles of the Triangle NOT adjacent to a given Exterior Angle are Remote Interior Angles.
![Page 39: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/39.jpg)
GEOMETRY 4.2
EXTERIOR ANGLE Theorem –
The measure of an EXTERIOR Angle of a Triangle
is EQUAL to
the SUM of the Measures of the TWO REMOTE Interior Angles.
![Page 40: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/40.jpg)
GEOMETRY 4.2
EXTERIOR ANGLE Theorem –
The measure of an EXTERIOR Angle of a Triangle
is EQUAL to
the SUM of the Measures of the TWO REMOTE Interior Angles.
PROVE It.
![Page 41: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/41.jpg)
GEOMETRY 4.2
![Page 42: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/42.jpg)
GEOMETRY 4.2
![Page 43: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/43.jpg)
GEOMETRY 4.2
605 2
135 1 3 4
![Page 44: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/44.jpg)
GEOMETRY 4.2
Definition: COROLLARY
A statement that can be easily proved using a theoremis called a COROLLARY.
1. The ACUTE ANGLES of a right triangle are COMPLEMENTARY.
2. There can be at most one right or obtuse angle in a triangle.
![Page 45: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/45.jpg)
GEOMETRY 4.2
![Page 46: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/46.jpg)
GEOMETRY 4.2 Solve for X in each Case.
![Page 47: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/47.jpg)
GEOMETRY 4.2
![Page 48: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/48.jpg)
GEOMETRY 4.2
![Page 49: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/49.jpg)
GEOMETRY 4.2
![Page 50: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/50.jpg)
GEOMETRY 4.2
![Page 51: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/51.jpg)
GEOMETRY 4.2
![Page 52: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/52.jpg)
GEOMETRY 4.2
![Page 53: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/53.jpg)
GEOMETRY 4.2
![Page 54: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/54.jpg)
GEOMETRY 4.2
![Page 55: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/55.jpg)
GEOMETRY 4.2
You should be able to:
PROVE the TOTAL DEGREES of INTERIOR ANGLES of a Triangle
DETERMINE the measure of the 3rd Angle of a Triangle
Determine the EXTERIOR ANGLE from the 2 REMOTE INTERIOR Angles
STATE the Corollaries (1) Acute angles of a Right Triangle (2) Number of Right/Obtuse Angles of a Triangle
![Page 56: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/56.jpg)
GEOMETRY 4.2
![Page 57: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/57.jpg)
GEOMETRY 4.2
![Page 58: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/58.jpg)
GEOMETRY 4.2
![Page 59: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/59.jpg)
GEOMETRY 4.2
![Page 60: Lesson: Objectives: 4.1 Classifying Triangles To IDENTIFY parts of triangles To CLASSIFY Triangles by their Parts](https://reader036.vdocuments.net/reader036/viewer/2022062423/5697bfda1a28abf838cb037f/html5/thumbnails/60.jpg)
Geometry 4.1