Geometry 5-5 Inequalities in Triangles Angles

TypeName Perpendicular Bisectors Circumcenter Angle BisectorsIncenter MediansCentroid AltitudesOrthocenter Points of Concurrency

TypeWhere CircumcenterEqual distance to vertices IncenterEqual distance to sides CentroidBalancing point 1/3 to side, 2/3 to vertex OrthocenterOn Euler Line, Nothing special Points of Concurrency Superpowers

TypeWhere CircumcenterInside Acute Outside Obtuse On hypotenuse of Right IncenterInside Triangle CentroidInside Triangle OrthocenterInside Acute Outside Obtuse On Right Angle Points of Concurrency Where they occur

Parts of Isosceles Triangle

Definition The next page has a visual definition of the word Adjacent. This definition is the same as when the word is used in English class. What is the English language definition of adjacent?

Triangle Exterior Angles

Review Recall the exterior angle theorem for triangles

Inequalities We can combine inequalities with known equations.

Theorem How do we combine the comparison property with the exterior angle theorem

Investigation - Supplies Ruler Protractors Computer Paper – 1 piece

Investigation Everyone Draw a triangle on a blank piece of paper

Investigation Use the protractor to measure all the angles in the triangle

Investigation Label the largest angle L Label the smallest angle S Label the middle sized angle M

Investigation Use the ruler to measure the lengths of the three sides

Investigation Label the largest side l Label the smallest side s Label the middle sized side m

Investigation Which side is opposite angle L?

Investigation Which side is opposite angle S? Is this true for all students? What conjecture can you make?

Theorem What is the converse of this theorem?

Theorem

Practice

Geometry 5-5b Inequalities in Triangles Sides

Triangle Inequalities What limitations are there on the lengths of triangle sides?

Triangle Inequalities Here are 21 different triangle with two sides, red and blue the same length

Investigation 1 - Supplies Spaghetti Handout – titled “What is the shortest path from A to B”

Investigation Break spaghetti pieces to match the lengths on the sheet, AC, AT, CT Try to arrange the pieces to make a triangle How many different triangles CAT could you form?

Investigation You should have been able to form exactly one triangle from the three pieces of spaghetti

Investigation Now break three more pieces to form the sides for the triangle FSH How many different triangles FSH could you form?

Investigation What must be true about the lengths of the three sides of a triangle in order for the three lengths to form a triangle?

Theorem

Practice

Homework Pages 277 – – 26 even, 32, 33, 48-55