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• Triangular Shape• Electromagnetism• The Lost Continent
of Atlantis• Portal to Another
Dimension
TRIANGLES
• 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 noncollinear points is called a vertex.
• The segments are called the sides.
Definition
vertex
vertex vertex
side side
side
NAMING A TRIANGLE AND ITS PARTS
• Triangle ABC / ΔABC
• Angles: A, B, & C
• Sides: AB, BC, & CA
a, b, & cA
B
C
c a
b
Note: Naming = Consecutive vertices (preferably clockwise)
TRIANGLE CLASSIFICATION (ACCDG. TO SIDES) pg 129
SCALENENo sides congruent
ISOSCELESAt least 2 sides congruent
EQUILATERALAll sides congruent
Using the Geoboards
TRIANGLE CLASSIFICATION (ACCDG. TO ANGLES) pg 129
ACUTE3 acute angles
RIGHT1 right angle
OBTUSE1 obtuse angle
EQUIANGULARAll angles congruent
┌
Paper-folding Investigation
Draw a triangle similar in shape to the ΔABC. Cut it out.
• Slide point A along AC toward point C until the fold passes through point B. The crease intersects AC at point D. Unfold the triangle.
A
B
C
A
B
CD
A
B
CD
• Bring point A to point D and crease.
• Bring points B and C to point D and crease.
A
B
CD
A B CD
What appears to be true about the sum of the measures of these angles three angles?
The sum of the measures of angles of a triangle is 180o.
A
B
CA B C
A + B + C = 180o
1 2
34 5
pg 110 - 111
Sample Problems
1. The angles of a triangle are in a ratio 3:4:5. Find the measures of all the angles.
2.(2x)o
(4x-8)o (5x-10)o
pg 111 - 112
TRUE or FALSE?
• 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 triangle, or at most one obtuse angle.
• The acute angles of a right triangle are complementary.
pg 114
EXTERIOR ANGLES OF A TRIANGLE
• ΔABC has been extended to form exterior angles:
1, 2, & 3.
• Each exterior angle has an adjacent interior angle and two remote interior angles.
• Example:– Exterior angle:– Adjacent interior angle:– Two remote angles:
A
BC
1
23
2
4 5
6
46 & 5
pg 116 - 117
Protractor investigation (exterior and remote interior angles)
• The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
• 1 = 4 + 5• 2 = 5 + 6• 3 = 4 + 6
A
BC
1
234 5
6
pg 117
5
4
Sample Problems: Solve for x.
1.
2.
pg 117
23o
40o
xo
84o
7xo 5xo