Chapter 4.1

1. Chapter 4.1 Common Core-G.SRT.5 Use congruence…criteria for triangles to solve problems and prove relationships in geometric figures. Objectives – To recognize congruent figures and their corresponding parts.

2. Ch 4.1 Notes Congruent Polygons – have congruent corresponding parts – their matching side and angles. When you name congruent polygons, you must list corresponding vertices in the same order.

3. 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

4. Chapter 4.2 Common Core -G.SRT.5 Use congruence…criteria for triangles to solve problems and prove relationships in geometric figures. Objectives – To prove two triangles congruent using SSS and SAS Postulates.

5. Ch 4.2 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 ≌. ≌

6. Chapter 4.3 Common Core - G.SRT.5 Use congruence…criteria for triangles to solve problems and prove relationships in geometric figures. Objectives – To prove two triangles congruent using ASA Postulate and AAS Theorem.

7. Ch 4.3 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 ≌. ≌

8. Chapter 4.4 Common Core - G.SRT.5 & G.CO.12 Use congruence…criteria for triangles to solve problems and prove relationships in geometric figures. Objectives – To use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles are congruent.

9. Ch 4.4 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

10. Chapter 4.5 Common Core Common Core- G.CO.10, G.CO.13 & G.SRT.5 Prove theorems about triangles…base angles of isosceles triangles are congruent. Objectives – To use and apply properties of isosceles and equilateral triangles.

11. Ch 4.5 Notes Isosceles Triangle Equilateral Triangle Leg Leg Base

12. 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. If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base. If then

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

15. Chapter 4.6 Common Core – G.SRT.5 Use congruence…criteria to solve problems and prove relationships in geometric figures. Objective – To prove right triangles congruent suing the Hypotenuse-Leg Theorem.

16. Ch 4.6 Notes 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

17. Chapter 4.7 Common Core – G.SRT.5 Use congruence…criteria to solve problems and prove relationships in geometric figures. Objectives – To identify congruent overlapping triangles. To prove two triangles congruent using other congruent triangles.

18. Ch 4.7 Notes Congruence in Overlapping Triangles - You can sometimes use the congruent corresponding parts of one pair of congruent triangles to prove another pair of triangles congruent. Review the five way to prove to two triangles congruent. 1) 2) 3) 4) 5)