1 / 15

Chapter 4 Notes

Chapter 4 Notes. Classify triangles according to their sides Equilateral Isosceles Scalene a ll 3 sides at least 2 no sides a re ≌ sides are ≌ are ≌. Classify triangles by their angles Acute Right Obtuse Equiangular (3 acute ∠’s) (1 rt. ∠) ( 1 obtuse ∠) (all the ∠’ s are =).

constance-murray
Download Presentation

Chapter 4 Notes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

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

  3. Right Triangle Isosceles Triangle Leg Hypotenuse Leg Leg Leg Base

  4. Interior Angles Exterior Angles

  5. 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.

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

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

  8. 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.

  9. 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 ≌. ≌

  10. 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 ≌. ≌

  11. 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.C.T.C

  12. 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

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

  14. 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

  15. 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.

More Related