1. 4.1 Triangles and Angles
October 6, 2011

2. Standard/Objectives:
Standard 3: Students will learn and apply geometric concepts.
Objectives:
Classify triangles by their sides and angles.
Find angle measures in triangles
DEFINITION: A triangle is a figure formed by three segments joining three non-collinear points.

3. Names of triangles
Triangles can be classified by the sides or by the angle
An Equilateral triangle has 3 congruent sides
An Isosceles Triangle has 2 congruent sides
A Scalene triangle has no congruent sides

4. Acute Triangle
M∠A = 42°
M∠B = 70°
M∠C = 68°
3 acute angles A B C

5. Equiangular triangle
3 congruent angles. An equiangular triangle is also acute.

6. Right Triangle
Obtuse Triangle
1 right angle
One obtuse angle

7. Parts of a triangle
Each of the three points joining the sides of a triangle is a vertex.(plural: vertices). A, B and C are vertices.
Two sides sharing a common vertex are adjacent sides.
The third is the side opposite an angle
adjacent
Side opposite A
adjacent
CA and BA are adjacent sides because they share vertex A. CB is the side opposite of vertex A.

8. Right Triangle
The side of the triangle opposite of the right angle is the hypotenuse of a right triangle. The sides that form the right angle are the legs.
hypotenuse
leg
leg

9. Isosceles Triangles
An isosceles triangle has only two congruent sides. These two sides are the legs of the isosceles triangle. The third is the base. A
leg
base B
leg C

10. Using Angle Measures of Triangles
Smiley faces are interior angles and hearts represent the exterior angles

11. Ex. 3 Finding an Angle Measure.
Exterior Angle Theorem: The measure of an exterior angle is the sum of the 2 NON-ADJACENT interior angles.
m1 = m A +m B
x + 65 = (2x + 10)
65 = x +10
55 = x
65 A
(2x+10) x 1 B

12. Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180°.
m∠A + m∠B + m∠C = 180°. A
40° B
60°
80° C