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Triangle Sum Properties

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### 4.1 notes

1. 1. 4.1 Triangle Sum Properties October 14, 2013 Chapter 4: Congruent Triangles Activity: Find the sum of the measures of the angles. Materials: Paper, Ruler & Scissors Draw 2 different sized triangles with one of the sides extended. Label the 4 angles. Cut out the triangles. A W B C D X Y Z 1st Triangle: Tear off the three corners. Place them next to each other on the extended line. Make a conjecture about the sum of the measures of interior <s 2nd Triangle: Tear off corners that aren't next to the exterior <s. Use them to fill the exterior <. Make a conjecture about the relationship between the measure of an exterior < and the nonadjacent interior <s. Conclusions: The sum of the measures of the interior <s of a triangle = 180. The measure of the exterior angle of a triangle the sum of the 2 nonadjacent interior <s. Oct 15­1:24 PM HW pg. 221 #8­18 evens, 21­26, 32 & 36 1
2. 2. 4.1 Triangle Sum Properties October 14, 2013 4­1 Triangle Sum Properties Objectives: To understand the sum of the measures of the angles of a  triangle. Classify Triangles by Sides Isosceles Scalene Equilateral  Classify Triangles by Angles Acute Right Obtuse Equiangular Oct 15­1:30 PM HW pg. 221 #8­18 evens, 21­26, 32 & 36 2
3. 3. 4.1 Triangle Sum Properties October 14, 2013 Triangle Sum Theorem The sum of the measures of the angles in every triangle is   _____. x = ______ xo 54o 39o n = ______ no 135o 30o Oct 17­9:52 AM HW pg. 221 #8­18 evens, 21­26, 32 & 36 3
4. 4. 4.1 Triangle Sum Properties October 14, 2013 Exterior Angle Theorem The measure of an exterior < of a triangle = the sum of the measures of the 2  nonadjacent interior <s. Exterior Angle Nonadjacent Interior Angles 2 1 3 Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary.  A <A + <C = 90 B C Sep 20­12:46 PM HW pg. 221 #8­18 evens, 21­26, 32 & 36 4
5. 5. 4.1 Triangle Sum Properties October 14, 2013 Find the measure of each numbered angle in the figure. 3 2 50o 1 78 o 120 o 4 5 56o 109o 95o 1 2 33 o 3 24o Sep 20­12:53 PM HW pg. 221 #8­18 evens, 21­26, 32 & 36 5
6. 6. 4.1 Triangle Sum Properties October 14, 2013 HW pg. 221 #8­18 evens,  21­26, 32 & 36 Oct 13­7:13 AM HW pg. 221 #8­18 evens, 21­26, 32 & 36 6