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Chapter 4. Congruent triangles
ANGLES
An angle is a set of points consisting of two rays, with a common endpoint
called THE VERTEX of the angle. The rays are callled SIDES or LEGS of
the angle
An angle can be classified according its measurement:

Acute angle:
Measure between 0 to 90 degrees

Right angle:
Measure 90 degrees

Obtuse angle: Measure between 90 to180 degrees

Straight angle: Measure 180 degrees

Reflex angle:
Measure between180 to 360 degrees
ANGLES
In addition, an angle can be classified according its characteristics and
relationship:

Adjacent angles:

Linear pair angles:
They have the same vertex and a common
side, but they don’t share any interior point.
Two adjacent angles which sum 180 degrees
ANGLES

Vertical angles:

Complementary angles: Angles adjacents or not, which sum 90
degrees
Are the opposite pair of angles formed when
two lines intersect. They are always congruent
ANGLES

Supplementary angles:
Are angles which sum is 180 degrees
ANGLES
Angles between parallel lines crossed by a transversal
-) Co-interior angles:
-) Co-exterior angles:
-) Vertical angles:
-) Corresponding angles:
-) Alternate interior angles:
-) Alternate exterior angles:
2-5,
1-6,
1-3,
1-5,
2-8,
1-7,
3-8
4-7
2-4, 5-7, 6-8
2-6, 4-8, 3-7
3-5
4-6
TRIANGLE
Definition:
3-sides geometric figure. The points
of the intersection of the sides are
called VERTEX.
TRIANGLES CLASSIFICATION: Sides
EQUILATERAL TRIANGLE
The Equilateral triangle has three equal sides and three equal angles.
Each angle is 60°
TRIANGLES CLASSIFICATION : Sides
ISOSCELES TRIANGLE
The Isosceles has two equal sides forming two equal angles with the
base.
TRIANGLES CLASSIFICATION : Sides
SCALENE TRIANGLE
The Scalene Triangle has no congruent sides. In other words, each
side must have a different length.
TRIANGLES CLASSIFICATION : Angles
ACUTE TRIANGLE
The Acute Triangle has three acute angles (an acute angle measures l
less than 90°)
TRIANGLES CLASSIFICATION : Angles
OBTUSE TRIANGLE
The Obtuse Triangle has an obtuse angle (an obtuse angle has more
than 90°). In the picture the shaded angle is the obtuse angle that
distinguishes this triangle
Since the total degrees in any triangle is 180°, an obtuse triangle can
only have one angle that measures more than 90°.
TRIANGLES CLASSIFICATION : Angles
RIGHT TRIANGLE
The Right Triangle has one 90° angle.
TRIANGLES CLASSIFICATION
TRIANGLES
Some properties:
A. The sum of the interior angles of a triangle is 180 degrees.
B. An exterior angle is the angle formed by a side and the extension of
one of its adjacent sides
In the graphic, 120 degree is an external angle
TRIANGLES
B. The Sum of an exterior and an interior angle of any triangle is 180
degrees; so they are supplementary angles
In the graphic, <y + 120 = 180degree
=> <y = 180 – 120 = 60 degree
where,
<y is an internal angle and
120 degree is an external angle
C. The measure of an exterior angle of a triangle is equal to the sum of
the two interior angles that are not adjacent to it.
In the graphic, 120 = x + 45
TRIANGLES
D. The shortest side is opposite to the smallest angle, and the longest side is
opposite to the longest angle
D. Any side of a triangle is shorter than the sum of the measure of the length of
the other two sides
CONGRUENT TRIANGLES
Triangles are congruent when they have exactly the same three
sides and exactly the same three angles.
These triangles are congruent: