1. Chapter 4. Congruent triangles

2. 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

3. ANGLES
In addition, an angle can be classified according its characteristics and
relationship:
Adjacent angles: They have the same vertex and a common
side, but they don’t share any interior point.
Linear pair angles: Two adjacent angles which sum 180 degrees

4. ANGLES
Vertical angles: Are the opposite pair of angles formed when two lines intersect. They are always congruent
Complementary angles: Angles adjacents or not, which sum degrees

5. ANGLES
Supplementary angles: Are angles which sum is 180 degrees

6. Congruents angles ANGLES
Angles between parallel lines crossed by a transversal
-) Co-interior angles: 2-5, 3-8
-) Co-exterior angles: 1-6, 4-7
-) Vertical angles: 1-3, 2-4, 5-7, 6-8
-) Corresponding angles: 1-5, 2-6, 4-8, 3-7
-) Alternate interior angles: 2-8, 3-5
-) Alternate exterior angles: 1-7, 4-6
Congruents
angles

7. TRIANGLE
Definition:
3-sides geometric figure. The points of the intersection of the sides are called VERTEX.

8. TRIANGLES CLASSIFICATION: Sides
EQUILATERAL TRIANGLE
The Equilateral triangle has three equal sides and three equal angles.
Each angle is 60°

9. TRIANGLES CLASSIFICATION : Sides
ISOSCELES TRIANGLE
The Isosceles has two equal sides forming two equal angles with the
base.

10. TRIANGLES CLASSIFICATION : Sides
SCALENE TRIANGLE
The Scalene Triangle has no congruent sides. In other words, each
side must have a different length.

11. TRIANGLES CLASSIFICATION : Angles
ACUTE TRIANGLE The Acute Triangle has three acute angles (an acute angle measures l less than 90°)

12. 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°.

13. TRIANGLES CLASSIFICATION : Angles
RIGHT TRIANGLE
The Right Triangle has one 90° angle.

14. TRIANGLES CLASSIFICATION

15. TRIANGLES Some properties:
The sum of the interior angles of a triangle is 180 degrees.
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

16. TRIANGLES
The Sum of an exterior and an interior angle of any triangle is 180 degrees; so they are supplementary angles
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
In the graphic, <y = 180degree
=> <y = 180 – 120 = 60 degree
where,
<y is an internal angle and
120 degree is an external angle

17. TRIANGLES
The shortest side is opposite to the smallest angle, and the longest side is opposite to the longest angle
Any side of a triangle is shorter than the sum of the measure of the length of the other two sides

18. CONGRUENT TRIANGLES
Triangles are congruent when they have exactly the same three
sides and exactly the same three angles.
These triangles are congruent: