The document defines a triangle as a figure formed by three line segments connecting three noncollinear points called vertices. The line segments are called sides. It notes that triangles are named using the consecutive vertices, preferably in clockwise order. Triangles can be scalene (no congruent sides), isosceles (at least two congruent sides), or equilateral (all sides congruent). Triangles can also be acute (all angles less than 90 degrees), right (one 90 degree angle), or obtuse (one angle greater than 90 degrees). The document also discusses properties of triangles such as angle sum, exterior angles, and using similar triangles.

2. Definition
• A set of points is a triangle if and only if it consists
of the figure formed by three segments connecting
three noncollinear points.
• Each of the three vertex
noncollinear points is called
a vertex.
vertex vertex
side
• The segments are called the
sides.

3. • Triangle ABC or ΔABC
B
• Angles: A, B, & C c a
• Sides: AB, BC, & CA A C
b
a, b, & c
Note: Naming = Consecutive vertices (preferably clockwise)

4. SCALENE ISOSCELES
No sides congruent At least 2 sides congruent
EQUILATERAL
All sides congruent

5. ACUTE RIGHT
3 acute angles 1 right angle
┌
OBTUSE EQUIANGULAR
1 obtuse angle All angles congruent

6. B
Draw a triangle similar in shape to
the ΔABC. Cut it out. A C
B
• Slide point A along AC toward
point C until the fold passes C
D
through point B. The crease A
intersects AC at point D. Unfold B
the triangle.
A C
D

7. • Bring point A to point D and B
crease.
A C
D
• Bring points B and C to point
D and crease.
A B C
D
What appears to be true about the sum of the measures of these angles three
angles?

8. The sum of the measures of angles of a
o
triangle is 180 .
B
4 3 5
B
1 2 A C
A C
o
A + B + C = 180

9. 1. The angles of a triangle are in a ratio 3:4:5.
Find the measures of all the angles.
2.
o
(2x)
o o
(4x-8) (5x-10)

10. • If two angles of one triangle are congruent to
two angles of a second triangle, then the third
angles are congruent.
• Each angle of an equiangular triangle measures
60o.
• In a triangle, there can be at most one right
angle, or at most one obtuse angle.
• The acute angles of a right triangle are
complementary.

11. • ΔABC has been
extended to form
exterior angles:
A
1, 2, & 3. 1
6
• Each exterior angle has
an adjacent interior
angle and two remote
B 4 5 3
interior angles. 2 C
• Example:
– Exterior angle: 2
– Adjacent interior angle: 4
– Two remote angles: 6& 5

12. • Exterior angles add to
360 degrees
A
1+ 2+ 3 = 360 1
6
• Each Exterior Angle
equals the sum of the
remote angles
B 4 5 3
2 C
• 1= 4+ 5
• 2= 5+ 6
• 3= 4+ 6

13. 1. 40o
23o xo
2. 84o
7xo 5xo

14. - Practice Pack: 28-50
- Textbook 196: 16, 24, 30-42 even, 47