JANUARY 7/8 WARM-UP  On your index card please finish the following statements with goals you would like to attain this semester in our geometry class and out of our geometry class. Try to challenge yourself, but make it realistic as well. Please write your name on it.  This semester in geometry I will….  This semester outside of geometry I will…

MS. YOUNG’S EXPECTATIONS: THE 5 P’S  Be Prompt: Arrive to class before the bell and turn in assignments on time  Be Prepared: Bring all necessary materials to class and come ready to learn each day  Be Productive: Follow directions, stay on task, do not cause disruptions, and try your best  Be Polite: Respect yourself, your classmates, your teachers, and your school. Use good manners and act professionally  Be Positive: Use uplifting words and tones when speaking, don’t complain, have confidence and hope

CLASS PROCEDURES  Entrance Agreement: Walk in and read the board, pick up materials, and start the warm up/study for quiz. Should be silent!  Class Agenda: Red time/Green time  Cell Phones/headphones: Not unless I have specifically said you may have it out  Sleeping/Head down: I will take your chair  Bathroom Passes: 5 bonus points each if not used

TRIANGLES A REVIEW [The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Opere Il Saggiatore p. 171

GUIDING QUESTION  What is critical thinking?

CLASSIFYING TRIANGLES - SIDES  Definitions:  Scalene: A triangle with no congruent sides  Isosceles: A triangle with at least two congruent sides  Equilateral: A triangle with three congruent sides  Fill in the blanks with one of the following options: sometimes, never, always  A scalene triangle is _____________________ an equilateral triangle  An equilateral is _____________________ always an isosceles triangle  An isosceles triangle is __________________ an equilateral triangle

CLASSIFYING TRIANGLES - ANGLES  Definitions:  Acute: a triangle with three acute angles  Equiangular triangle: a triangle with congruent angles  Right: a triangle with one right angle  Obtuse: a triangle with one obtuse angles  Is it possible to have more than one obtuse angle?  Fill in the blanks with one of the following options: sometimes, never, always  An obtuse triangle is _____________________ an acute triangle  An acute triangle is ______________________ an equiangular triangle  And equiangular triangle is ___________________ an acute triangle

RELATING SIDE LENGTH AND ANGLE MEASURE  Theorem 5.10  If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side  Theorem 5.11  If on angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle 60˚ 70˚ 50˚ Identify the largest and smallest sides:

PRACTICE  Work with your group on the classifying triangles practice

TRIANGLE INEQUALITIES  Theorem 5.12 Triangle Inequality Theorem:  The sum of the lengths of any two sides of a triangle is greater than the length of the third side

A TRIANGLE HAS ONE SIDE LENGTH 12 AND ANOTHER OF LENGTH 8. DESCRIBE THE POSSIBLE LENGTHS OF THE THIRD SIDE. Scenario 1: missing side is a small value x+8>12 Scenario 2: missing side is largest value 8+12>x 12 8 x x 8

INEQUALITIES IN TWO TRIANGLES Theorem 5.13 Hinge Theorem  If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. Theorem 5.14 Converse of Hinge Theorem  If two side of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second. 12 8

PRACTICE  Work with your group on the triangle inequalities practice

INTERIOR AND EXTERIOR ANGLES OF A TRIANGLE Interior Angles  The original angles within a triangle when sides of the polygon are extended Exterior Angles  The angle that form linear pairs with the interior angles are the exterior angles

INTERIOR AND EXTERIOR ANGLES OF A TRIANGLE Triangle Sum Theorem  The sum of the measures of the interior angles of a triangle is 180˚ Exterior Angle Theorem  The measure of an exterior angle of a triangle is equal to the sum of the measure of the two nonadjacent interior angles

PRACTICE  Work with your group on the interior/exterior angles of a triangle practice

HOMEWORK  Complete any practice problems you did not complete. Prepare for the quiz next class period.