2What you’ll learnHow to identify and name the parts of a triangle.How to identify and classify triangles by angles.How to identify and classify triangles by sides.
3Vocabulary Sides of a triangle Vertices of a triangle Acute triangle Obtuse triangleRight triangleEquiangular triangleScalene triangleIsosceles triangleEquilateral triangle
4The vertices of this triangle are: The parts of a triangleThe vertices of a triangle are the corner points joining the sides of the trianglePoints are named with capital printed lettersOne corner is called a VERTEX more than one, VERTICESFSHThe vertices of this triangle are:F,S,and H
5The sides of this triangle are: The parts of a triangleThe sides are line segmentsSegments are named by endpointsSides will have measure (like inches)The sides of this triangle are:FSHFS,SH,and HF
6The angles of this triangle are: The parts of a triangleEvery triangle will have three anglesAngles are named by “” with three points (vertex in middle) , “” with just the vertex, or “” with a numberThe angles of this triangle are:FSHF or SFH,S or FSH,and H or SHF
7You must include the Δ symbol NAMING A TRIANGLETriangles are named by their verticesCTHIS TRIANGLE CAN BE CALLEDΔACTΔTACATΔCATYou must include the Δ symbol
8Classifying Triangles by Angles Acute Triangles—triangles with all 3 angles measuring less than 90°Obtuse triangles—triangles with exactly ONE angle measuring between 90° and 180°Right Triangles– triangles with exactly ONE right angle (marked with a box)Equiangular Triangles—triangle with all angles exactly the same measure (all are congruent to each other)
9Classifying Triangles by Sides Scalene Triangles—triangles with no 3 sides of equal measure (no congruent sides)Isosceles triangles—triangles with at least TWO sides of equal measure (2 congruent sides)Equilateral Triangles—triangle with all sides exactly the same measure (all 3 sides congruent to each other)
10Parts of an Isosceles Triangle Vertex angleVertex angleVertex angleThe vertex angle is always the angle between the two congruent sides; the other angles are called base angles.
11Example Problem #1: Find x if ΔJMN is isosceles with JM = MN. M 2x – 5
12Example Problem #2:ΔFGH is equilateral. With FG = x + 5, GH = 3x – 9, and FH = 2x Find x and the length of each sideGx + 53x – 9FH2x - 2
13Example Problem #3: Classify ΔRST by its sides. R(0, 2) S(2, 5)
14Have you learnedHow to identify and name the parts of a triangle?How to identify and classify triangles by angles?How to identify and classify triangles by sides?Assignment:NON-PROOF:Worksheet 4-1PROOF: P. 181(22-44E, 50-56E)