4-1
DESCRIPTION
4-1. Classifying Triangles. Holt Geometry. Warm Up. Lesson Presentation. Lesson Quiz. Do Now Classify each angle as acute, obtuse, or right. 1. 2. 3. 4. If the perimeter is 47, find x and the lengths of the three sides. right. acute. obtuse. x = 5; 8; 16; 23. Objectives. - PowerPoint PPT PresentationTRANSCRIPT
Holt Geometry
4-1 Classifying Triangles4-1 Classifying Triangles
Holt Geometry
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt Geometry
4-1 Classifying Triangles
Do NowClassify each angle as acute, obtuse, or right.
1. 2.
3.
4. If the perimeter is 47, find x and the lengths of the three sides.
right acute
x = 5; 8; 16; 23
obtuse
Holt Geometry
4-1 Classifying Triangles
Classify triangles by their angle measures and side lengths.
Use triangle classification to find angle measures and side lengths.
Objectives
Holt Geometry
4-1 Classifying Triangles
acute triangleequiangular triangleright triangleobtuse triangleequilateral triangleisosceles trianglescalene triangle
Vocabulary
Holt Geometry
4-1 Classifying Triangles
Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths.
Holt Geometry
4-1 Classifying Triangles
B
AC
AB, BC, and AC are the sides of ABC.
A, B, C are the triangle's vertices.
Holt Geometry
4-1 Classifying Triangles
Acute Triangle
Three acute angles
Triangle Classification By Angle Measures
Holt Geometry
4-1 Classifying Triangles
Equiangular Triangle
Three congruent acute angles
Triangle Classification By Angle Measures
Holt Geometry
4-1 Classifying Triangles
Right Triangle
One right angle
Triangle Classification By Angle Measures
Holt Geometry
4-1 Classifying Triangles
Obtuse Triangle
One obtuse angle
Triangle Classification By Angle Measures
Holt Geometry
4-1 Classifying Triangles
Classify BDC by its angle measures.
Example 1: Classifying Triangles by Angle Measures
Classify ABD by its angle measures.
obtuse
acute
Holt Geometry
4-1 Classifying Triangles
Classify FHG by its angle measures.
Example 2
equiangular
Holt Geometry
4-1 Classifying Triangles
Equilateral Triangle
Three congruent sides
Triangle Classification By Side Lengths
Holt Geometry
4-1 Classifying Triangles
Isosceles Triangle
At least two congruent sides
Triangle Classification By Side Lengths
Holt Geometry
4-1 Classifying Triangles
Scalene Triangle
No congruent sides
Triangle Classification By Side Lengths
Holt Geometry
4-1 Classifying Triangles
Remember!When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent.
Holt Geometry
4-1 Classifying Triangles
Classify EHF by its side lengths.
Example 3: Classifying Triangles by Side Lengths
Classify EHG by its side lengths.isosceles
scalene
Holt Geometry
4-1 Classifying Triangles
Classify ACD by its side lengths.
Example 4
isosceles
Holt Geometry
4-1 Classifying Triangles
Find the side lengths of JKL.
Example 5: Using Triangle Classification
JK=KL=23.3
JL = 44.5
Holt Geometry
4-1 Classifying Triangles
Find the side lengths of equilateral FGH.
Example 6
All = 17
Holt Geometry
4-1 Classifying Triangles
A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the triangle is 18 feet long. How many triangles can be formed from 420 feet of steel beam?
Example 7: Application
7
Holt Geometry
4-1 Classifying Triangles
Activity #1 180321 mm
!Behold
1
1
2
2
3
3
Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180˚.
Holt Geometry
4-1 Classifying Triangles
Activity #2 (alternative)
1
2 3123
1
2 3
180321 mm
!Behold
Holt Geometry
4-1 Classifying Triangles
Triangle Inequality TheoremThe sum of the lengths of any two sides of a triangle is greater than the length of the third side. The smallest angle is opposite the shortest side while the largest angle is opposite the longest side.
Y
X
ZYZXYXZ
XYXZYZ
XZYZXY
Holt Geometry
4-1 Classifying TrianglesList the angles from smallest to largest:
CBA
C
B
A
2
6
5
B
C
A
5
13
12 BCA
Holt Geometry
4-1 Classifying TrianglesCan a triangle have the given lengths?
! 732
237
327
NO
BUT
C
B
A
2
7
3
! 20119 NO
C
B
A
9
20
11
Holt Geometry
4-1 Classifying TrianglesCan a triangle have the given lengths?
! NO
C
B
A
3
8
4
!YES
C
B
A
3
11
10
Holt Geometry
4-1 Classifying TrianglesDescribe possible lengths for the third side:
9, 12
213
21129
3912
3129
x
xx
xx
xx
Holt Geometry
4-1 Classifying Triangles
Describe possible lengths for the third side:
4, 15
3, 4
1911 x
71 x
Holt Geometry
4-1 Classifying Triangles
Classify by Angles
60˚
60˚
60˚
Equiangular
Acute Right Obtuse
Classify by Sides
Equilateral
IsoscelesScalene
Holt Geometry
4-1 Classifying Triangles
Classify by angles:
67˚ 48˚
x
Acute
Holt Geometry
4-1 Classifying Triangles
Classify by angles:
x
z
y
70˚
Right
Holt Geometry
4-1 Classifying Triangles
Classify by angles and sides
2
4
120˚
5 Obtuse / Scalene
Right/ IsoscelesEquiangular/ Equilateral
Holt Geometry
4-1 Classifying Triangles
Classify by angles and sides
125˚
X
Right / Scalene
Holt Geometry
4-1 Classifying Triangles
A triangle with a 90˚ angle has sides that are 3 cm, 4 cm, and 5 cm long. Classify the triangle by its angles and sides.
Right / Scalene
Holt Geometry
4-1 Classifying Triangles
Classify by angles and sides:
70˚ 42˚
y
Acute / Scalene
Holt Geometry
4-1 Classifying Triangles
x
160˚125˚
Obtuse / Scalene
Classify by angles and sides: