2.  Objective: we will be able to classify triangles by their angles and by their sides. A B C The vertices of a triangle are labeled with upper case letters. The sides are ____, ____, & _____ All s have at least two __________ but the third is used to classify the Classify s by Angles Classify s by Sides Has ___ that is a right (90 degrees). An ______________ is a special kind of _______________. acute right acute obtuse scaleneisosceles equilateral equiangular isosceles 1 1 3 0 2 3

3. Q R S Example 1: Find x and the measure of each side of equilateral triangle QRS, if QR = 4x, RS = 2x + 1, and QS = 6x – 1. Example 2: Find the measures of the sides of LMN. L(4, 4), M(-1,-3), & N(8, -1) Classify the triangle by its sides. x = ½ ; sides = 2

4.  Objective: we will be able to apply the Angle Sum Theorem and the Exterior Angle Theorem to find the measures of angles in a triangle. “Angle Sum Theorem” The sum of the measures of the angles of a = _____ a b c When the measures of 2 of the angles are known, how can we find the measure of the 3 rd angle? a + b + c = _____ 1 2 3 a b a + b = _____ Example: Look at proof page 185 “Third Angle Theorem” A B C D E F A B C D E F

5.  Objective: we will be able name and label corresponding parts of congruent triangles and identify congruence transformations. triangles have the same and same Congruent sizeshape A B C “Exterior Angle Theorem” a b c d a + b = _____ The measure of an exterior angle of a is equal to the sum of the measures of the two remote interior angles. Example: 1 2 3 4 5 D E F then,and, Two triangles are _____ if and only if their corresponding parts are _____. Definition of congruent triangles: Corresponding Parts of Congruent Triangles are Congruent = _____________ C P C T C Congruence transformations: ________, ________, or ________ (page 194 ). slide flipturn Hands on Activity p.184

6.  Objective: we will be able use the SSS and the SAS Postulates to test for triangle congruence. SIDE-SIDE-SIDE Congruence (SSS) ABC ___ XYZ given : prove : proof : statements reasons 1. 2. 3. 1. 2. 3. B A Y C

7. SIDE-ANGLE-SIDE Congruence (SAS) “ ________________” : the angle formed by two sides (in between). ABC ___ XYZ Review theorems: Midpoint Theorem Reflexive Property All right angles are congruent Definition of congruent segments Definition of congruent angles Definition of angle bisector Alternate interior angles Vertical angles are congruent Def. of Congruent Triangles (CPCTC) Included angle

8.  Objective: we will be able use the ASA and the AAS Postulates to test for triangle congruence. ANGLE-SIDE-ANGLE Congruence (SAS) ABC ___ XYZ given : prove : proof : statements reasons 1. 2. 3. 1. 2. 3. B R P C 4. 5. 4. 5. “ _________________” : the side formed by two angles (in between). Included side example: Name the congruent angles and sides for the pair of congruent triangles.

9. ANGLE-ANGLE-SIDE Congruence (AAS) ABC ___ XYZ given : prove : proof : statements reasons 1. 2. 3. 1. 2. 3. B D A C 4. “ ____________________” : the side not between the angles designated. Non-included side example: Name the congruent angles and sides for the pair of congruent triangles. F angles sides u N D A Y E

10. Proof Puzzle Directions: 1. Copy the Given and Prove statements from the envelope onto your sheet. 2. Copy the diagram (using a ruler) and label the drawing according to the given information. 3. Read what 2 triangles you are trying to prove are congruent. 5. Concentrate on 3 sides or a side-angle-side correspondence. 6. Once you think you have the proof arranged, raise you hand to get it checked, and then copy it onto your note sheet.