1. 4.1 Warm up 1. Using deductive reasoning prove the following: 4x -6 = 2(x + 9) 2) 6, 17, 28, 39….. Find the function rule and the 50th term 3) With parallel lines, certain relationship exist for the type of angles formed. List the type of angles that are created and their relationship.

2. Answers 1)4x-6 = 2(x+9) Given 4x-6 = 2x + 18 Distributive Prop 2x – 6 = 18Subtraction prop. of equality 2x = 24 Addition prop. of equality x = 12 Division prop. of equality 2)6, 17, 28, 39…… nth term = f(n) = 11n – 5 50 th term = 545 3)Vertical angles, corresponding angles, alt. exterior, alt interior are congruent Same side interior, same side exterior, linear pairs add to 180

3. Sub groups -Scalene Triangleno congruent sides. Equilateral Triangleall sides are congruent. Isosceles Triangleat least 2 congruent sides. Triangles- Come in 3 types: Acute: Obtuse:Right: An acute triangle has 3 acute angles An obtuse triangle has 1 obtuse angle A right triangle has 1 right angle. You can have Scalene and Isosceles of each type of triangle!

4. Triangles Acute ScaleneIsosceles Equilatera l Obtuse ScaleneIsosceles Right ScaleneIsosceles List each type of triangle

5. Triangles Sketch each type of triangle in the box

6. Ex. 1 - Triangles How do I sketch, label, and mark each figure? A) Right Isosceles triangle SUN with SU = UN. B) Obtuse Isosceles triangle SEA with SE = EA.

7. Triangles class work! Page 64-65 Questions #2-20 More to come……stay tuned!

8. 4.1 Triangle Congruence Year 2 Geometry

9. Materials You will need: Protractor Scissors

10. Investigation #1 Draw a triangle using your straight edge of the protractor. Make a variety of sizes! Measure each angle of the triangle to the nearest 10°. The sum of the interior angles equals to ? Cut out the triangle (around the perimeter). Cut 2 of the vertices (angles) from the triangle. Line up all three vertices. What do you notice? 180° They form a line. (180°)

11. Investigation #1 – continued Paste the three vertices lined up in your notes and complete the following conjecture. Triangle Sum Conjecture The sum of the measures of the interior angles in every triangle is _______. 180°

12. Third Angle Conjecture If two angles of one triangle are equal in measure to two angles in another triangle, then the third angle in each triangle is ___________________________? equal in measure

13. Example #1 52° 55° x

14. Example #2 120° 130° 100° z 60° 50° x

15. Example #3 x 2x-9 x+7 A B C

16. Example #4 48° w x x

17. Example #5 3x+132x+7 4x+25 AC B

18. Example 6 With a partner create your own problem with triangles similar to the previous examples to share with your group.

19. Summary Write the Triangle Sum Conjecture in your own words.

20. In – Class Work Lesson 4.1 – workbook Homework: Triangle Sum HW pg 201-202 2-5,8,9, 14-16