Download Classifiy Measure and Special Segments in Triangles.notebook

Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Triangles
Triangle ABC ABC
Sides: Segments that make a triangle.
A
B
C
Vertices: Points where sides meet.
1
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Scalene: no congruent sides
(
Isosceles: at least 2 congruent sides
Equilateral: all 3 congruent sides
(
(
Equiangular: all 3 congruent angles
2
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Try These:Classify each triangle as equilateral, isosceles, or scalene.
8
10
8
6
12
8
7
4
4
3
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
(
Corollary 4­3
A triangle is equilateral iff equiangluar.
(
(
Corollary 4­4
Each angle of an equilateral triangle measures 60 degrees.
60
60
60
4
Classifiy Measure and Special Segments in Triangles.notebook
Acute
Triangle:
3 acute
angles
October 29, 2013
Obtuse
Triangle:
Right
Triangle:
1 obtuse
angle
1 right
angle
5
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Try These:Classify each triangle as acute, obtuse, right, or equiangular
51
60
60
84
45
30
115
60
60
30
35
6
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
TRUE or FALSE
______ a.) All isosceles triangles are acute.
______ b.) An acute triangle can be equilateral.
______ c.) A scalene triangle is never obtuse.
______ d.) A right triangle can be isosceles.
7
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
RIGHT TRIANGLE
Hypotenuse: Side opposite the right
angle in a right triangle
Corollary: The acute angles of a
right triangle are complementary.
Corollary: There can be at most
one right or obtuse angle in a
triangle.
Legs: the two sides that make
up the right angle in a right triangle.
8
Classifiy Measure and Special Segments in Triangles.notebook
ISOSCELES TRIANGLE
Base Angles: The two angles
formed by the base and one
of the congruent sides.
Vertex Angle: Angles formed by congruent sides in an isosceles triangle.
(
(
October 29, 2013
Base: The side opposite the vertex angle in an isosceles triangle.
9
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
.
Isosceles Theorem: If two sides of a
triangle are ≅, then the angles opposite them
are also ≅.
* Converse is also true * We will prove in the next unit (
(
10
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Example Find the length of the legs.
B
C
x + 10
4x ­ 14
A
11
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Example Find "x".
5x ­ 5
A
B
3x + 5
C
12
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Example (
Find x.
­ 6
3x (
x + 10
13
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Example Find x.
4x ­ 20
3x
14
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Example < D is the vertex angle of isosceles triangle DEF.
D
E
F
m < E = 2x + 40
m < F = 3x + 22
15
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Example Find x.
30
(
4x + 2
6x ­
(
16
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Example If < X is the vertex angle of an isosceles triangle, find m< Y and m< Z if m< X = 54.
X
Y
Z
17
Classifiy Measure and Special Segments in Triangles.notebook
October 29, 2013
Example Find "x".
A
2x + 5
B
x + 35
C
18