Chapter 4 Notes Classify triangles according to their sides Equilateral Isosceles Scalene all 3 sides at least 2 no sides are ≌ sides are ≌ are ≌

Classify triangles by their angles Acute Right Obtuse Equiangular (3 acute ∠’s) (1 rt. ∠) ( 1 obtuse ∠) (all the ∠’s are =)

Right Triangle Isosceles Triangle Leg Hypotenuse Leg Leg Leg Base

Interior Angles Exterior Angles

Triangle Sum Thm – The sum of the interior angles of a triangle is 180° Exterior Angle Thm – The measure of an exterior angle of a triangle is equal to the sum of the measure of the 2 nonadjacent interior angles.

Corollary to the Triangle Sum Thm – the acute angles of a right triangle are complementary. A C B m∠A + m∠B = 90°

Chapter 4.2 Notes If 2 triangles are ≌ then they have 3 corres-ponding sides and 3 corresponding ∠’s. Corr. Sides Corr. Angles 1) 2) 3) A X B C Y Z

Third Angle Thm – if 2 ∠’s of one triangle are congruent to 2 ∠’s of another triangle, then the third angles are also congruent. B E A C D F If ∠A ≌ ∠D and ∠B ≌ ∠E, then ∠C ≌ ∠F.

Chapter 4.3 Notes Side-Side-Side Post. (SSS) – if 3 sides of one triangle are ≌ to 3 sides of another triangle, then the 2 triangles are congruent ≌ Side-Angle-Side Post. (SAS) – if 2 sides and the included ∠ of one triangle are ≌ to 2 side and the included angle of a second triangle, then the 2 triangles are ≌.

Chapter 4.4 Notes Angle-Side-Angle Post. (ASA) – if 2 ∠’s and the included side of one triangle are ≌ to 2 ∠’s and the included side of a second triangle, then the 2 triangles are congruent ≌ Angle-Angle-Side Post. (AAS) – if 2 ∠’s and a nonincluded side of one triangle are ≌ to 2 ∠’s and the corresponding nonincluded side of a second triangle, then the 2 triangles are ≌.

Chapter 4.5 Notes Once you have 2 triangles ≌ then you can say anything you want about their corresponding parts. (It is called Corresponding Parts of Congruent Triangles are Congruent) *You can use the acronym C.P.T.C

Chapter 4.6 Base Angle Thm – if 2 sides of a triangle are ≌, then the angles opposite them are ≌. If then If AB ≌ AC, the ∠B ≌ ∠C Converse of the Base Angles Thm – If 2 ∠’s of a triangle are ≌, then the sides opposite them are ≌. If then

Corollaries If a triangle is equilateral, then it is equiangular Corollaries If a triangle is equilateral, then it is equiangular. If then If a triangle is equiangular, then it is equilateral.

Hypotenuse-Leg Congruence Thm (HL) If the hypotenuse and a leg of a right triangle are ≌ to the hypotenuse and a leg of a second right triangle, then the 2 triangles are ≌. A D B C E F If BC ≌ EF and AC ≌ DF, then ABC ≌ DEF

Chapter 4.7 Notes Coordinate Proof – involves placing geometric figures in a coordinate plane. Then you can use the Distance Formula and the Midpoint Formula, as well as postulates and theorems, to prove statements about the figures.