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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. Answers 1) 4x-6 = 2(x+9) 4x-6 = 2x + 18 Given Distributive Prop 2x – 6 = 18 Subtraction 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 50th term = 545 3) Vertical angles, corresponding angles, alt. exterior, alt interior are congruent Same side interior, same side exterior, linear pairs add to 180 Triangles- Come in 3 types: Obtuse: Acute: An acute triangle has 3 acute angles An obtuse triangle has 1 obtuse angle Right: A right triangle has 1 right angle. Sub groups -Scalene Triangle no congruent sides. Equilateral all sides are congruent. Isosceles Triangle Triangle at least 2 congruent sides. You can have Scalene and Isosceles of each type of triangle! Triangles List each type of triangle Acute Scalene Obtuse Scalene Isosceles Equilateral Right Isosceles Scalene Isosceles Triangles Sketch each type of triangle in the box 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. Triangles class work! Page 64-65 Questions #2-20 More to come……stay tuned! 4.1 Triangle Congruence Year 2 Geometry Materials You will need: Protractor Scissors 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). 180° Cut 2 of the vertices (angles) from the triangle. Line up all three vertices. What do you notice? They form a line. (180°) 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 180° in every triangle is _______. 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 ___________________________? Example #1 x 52 55 180 x x 107 180 52° 55° x 73 Example #2 x 60 50 180 z x 130° 50° x 110 180 x 70 100° 60° 120° z 70 180 z 110 Example #3 B Find mA, mB, mC. x+7 x x 7 2 x 9 180 4 x 2 180 4 x 182 x 45.5 x A 2x-9 C mA 45.5 mB 52.5 mC 82 Example #4 Find w. w x 48° x 48 x x 180 48 2 x 180 2 x 132 x 66 w 66 90 w 24 Example #5 Find mA, mB, mC. 3x 13 4 x 25 2 x 7 180 9 x 45 180 9 x 135 x 15 B 4x+25 3x+13 A mA 58 mB 85 2x+7 C mC 37 Example 6 With a partner create your own problem with triangles similar to the previous examples to share with your group. Summary Write the Triangle Sum Conjecture in your own words. In – Class Work Lesson 4.1 – workbook Homework: Triangle Sum HW pg 201-202 2-5,8,9, 14-16