Transcript 4.1 Triangles and Angles

4.1 Triangles and Angles
Interior and Exterior Angles
Types of Triangles
Definition of a triangle
A triangle is three segments joined at three
noncollinear end points.
vertex
side
side
adjacent sides
vertex
side
vertex
Types of Triangles by Sides
3 Sides congruent → Equilateral
Types of Triangles by Sides
2 Sides congruent → Isosceles
Part of the
Isosceles Triangle
leg
leg
base
Types of Triangles by Sides
No Sides congruent → Scalene
Types of Triangles by Sides
3 Sides congruent → Equilateral
2 Sides congruent → Isosceles
No Sides congruent → Scalene
Types of Triangle by Angles
All Angles less than 90 degrees → Acute
Types of Triangle by Angles
One Angle greater
than 90 degrees → Obtuse
Types of Triangle by Angles
One Angle equal to 90 degrees → Right
Parts of the Right Triangle
Across from the right angle is the
hypotenuse.
hypotenuse
leg
leg
Equiangluar
All the angles are Equal
Interior Angles vs. Exterior Angles
Interior Angles in Pink
Exterior Angles
In light green
A Theorem about Angles in a Triangle
The interior angles in a triangle add to 180º
110
x
25
Solve for x
Theorem about an exterior angle
The measure of an exterior angle equals the
measure of the two nonadjecent interior
angles.
86
57  86  143
57
Solve for x
x
79
14
Corollary for the fact that interior
angles add to 180º
The acute angles of a Right triangle are
complementary.
90  x
x
Homework
Page 198 - 201
# 10 - 15,
16 - 38 even,
42, 49, 50
Homework
Page 198 - 201
# 17 – 43 odd,
45 – 47,
52 - 68