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 or 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)

SCALENENo sides congruent

ISOSCELESAt least 2 sides congruent

EQUILATERALAll sides congruent

TRIANGLE CLASSIFICATION (ACCDG. TO ANGLES)

ACUTE3 acute angles

RIGHT1 right angle

OBTUSE1 obtuse angle

EQUIANGULARAll angles congruent

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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

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

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 angle, or at most one obtuse angle.

• The acute angles of a right triangle are complementary.

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

EXTERIOR ANGLES OF A TRIANGLE

• Exterior angles add to 360 degrees

1 + 2 + 3 = 360

• Each Exterior Angle equals the sum of the remote angles

• 1 = 4 + 5• 2 = 5 + 6• 3 = 4 + 6

A

BC

1

234 5

6

Sample Problems: Solve for x.

1.

2.

23o

40o

xo

84o

7xo 5xo

Practice

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