TRIANGLES C.N.Colón Geometry St. Barnabas H.S. Bronx, NY

Classifying Triangles What You'll Learn You will learn to identify the parts of triangles and to classify triangles by their parts. A polygon is a closed figure in a plane that is the union of line segments such that the line segments intersect only at their endpoints and no segments sharing a common endpoint are collinear. three In geometry, a triangle is a polygon formed when _____ noncollinear points are connected by segments. E D F The vertex of each angle is a vertex of the triangle. Each side is included between two vertices. Each pair of segments forms an angle of the triangle. The angle is included between the lines.

Included Angles C is the included angle of CA and CB A is the included angle of AB and AC B is the included angle of BA and BC

Included Sides The side of a triangle that falls between two given angles is called the ___________ of the angles. included side It is the one side common to both angles. A B C AC is the included side of A and C CB is the included side of C and B AB is the included side of A and B You can show that two triangles are congruent by using _________ and the ___________ of the triangles. two angles included side

Classifying Triangles Triangles are named by the letters at their vertices. Triangle DEF, written ______, is shown below. ΔDEF vertex The sides are: EF, FD, and DE. E D F angle The vertices are: D, E, and F. The angles are: E, F, and D. side You already know that angles can be acute, obtuse, or right. Triangles can also be classified by their angles. All triangles have at least two _____ angles. acute The third angle is either _____, ______, or _____. acute obtuse right

Classifying Triangles Classified by Angles acute triangle obtuse triangle right triangle 60° 80° 120° 17° 43° 30° 60° 40° 3rd angle is _____ 3rd angle is ______ 3rd angle is ____ acute obtuse right

Classifying Triangles Classified by Sides scalene isosceles equilateral ___ sides congruent no __________ sides congruent at least two ___ sides congruent all

Classifying Triangles The angle formed by the congruent sides is called the ___________. vertex angle The two angles formed by the base and one of the congruent sides are called ___________. The congruent sides are called legs. base angles leg leg The side opposite the vertex angle is called the _____. base

An equiangular triangle is a triangle that has three congruent angles. Angles of a Triangle Theorem An equiangular triangle is a triangle that has three congruent angles. The measure of each angle of an equiangular triangle is 60. x° 3x = 180 x = 60

Right Triangle A hypotenuse leg B C leg

The acute angles of a right triangle are complementary. Angles of a Triangle Theorem The acute angles of a right triangle are complementary. x° y° x + y = 90

You will learn to use the Angle Sum Theorem. Angles of a Triangle What You'll Learn You will learn to use the Angle Sum Theorem. 1) On a piece of paper, draw a triangle. 2) Place a dot close to the center (interior) of the triangle. 3) After marking all of the angles, tear the triangle into three pieces. then rotate them, laying the marked angles next to each other. Make a conjecture about the sum of the angle measures of the triangle.

The sum of the measures of the angles of a triangle is 180. Angle Sum Theorem The sum of the measures of the angles of a triangle is 180. z° x° y° x + y + z = 180

In Geometric Diagrams You can ASSUME You CANNOT ASSUME A line segment is a part of a straight line. The measure of one segment is equal to, less than, or greater than that of another segment The point where two segments intersect is a point on each segment A point is a midpoint of a line segment Points on a line segment are between the endpoints of that segment Lines are perpendicular or angles are right . Must have a bracket square at angle. Points on a line are collinear Triangle is isosceles or equilateral. Must be shown with tick marks. A ray in the interior of an angle with its endpoint at the vertex separates the angle into two adjacent angles The measure of an angle is equal to, less than, or greater than that of another angle another . A given quadrilateral is a parallelogram, rectangle, square rhombus or trapezoid

HOMEWORK p. 27 #3-18 (e)