Topic 2 Angle Properties in Triangles Unit 2 Topic 2

Explore Use the protractor to measure each of the interior angles in  ABC. By inductive reasoning, make a conjecture about the sum of the interior angles of a triangle. Try this on your own first!!!!

Explore Use the protractor to measure each of the interior angles in  ABC. By inductive reasoning, make a conjecture about the sum of the interior angles of a triangle. 72  46  62  The sum of the three angles in a triangle add up to 180 °.

Explore You can use deductive reasoning to prove the interior angles of  ABC add to 180 °. In the figure on the right, line DE is parallel to side BC, complete the proof below by filling in the missing reasons. Try this on your own first!!!!

Explore You can use deductive reasoning to prove the interior angles of  ABC add to 180 °. In the figure on the right, line DE is parallel to side BC, complete the proof below by filling in the missing reasons. Alternate interior angles are equal Straight line angles add to 180 °

The sum of the three interior angles of a triangle is 180 °, as shown in the figure on the right. This is called the triangle sum theorem. Information

Example 1 Finding Missing Angles in a Triangle a) Determine the missing angles. Try this on your own first!!!!

Example 1 Finding Missing Angles in a Triangle a) Determine the missing angles.

Example 2 Determining Missing Angles Using Properties of Parallel Lines a) Try this on your own first!!!! StatementReason x yz 50  65 

Example 2a: Solution StatementReason z= 65 ⁰ Angles that form a line are supplementary. x= 65 ⁰ Alternate interior angles are equal. y= 50 ⁰ The angles in a triangle must add to 180 ⁰. x yz 50  65 

Example 2b Determining Missing Angles Using Properties of Parallel Lines Try this on your own first!!!! StatementReason 67  39  20  R L z x y

Example 2b: Solution 67  39  20  R L z x y StatementReason Alternate interior angles are equal. Triangle sum theorem Straight line angles sum to 180 °.

Example 3a Determining a Formula for the Sum of the Interior Angles of a Triangle Try this on your own first!!!! A polygon is a closed two-dimensional shape with straight sides. A triangle is a three-sided polygon. By the triangle sum theorem, the angles in a triangle always add up to 180°. a) Using the triangle sum theorem, complete the table. The first three rows are completed for you.

Example 3a: Solution 4 5

Example 3b & c Determining a Formula for the Sum of the Interior Angles of a Triangle b) Based on the table, make a conjecture about the relationship between the sum of the measures of the interior angles and the number of sides of the polygon. c) A Canadian loonie coin is an example of a polygon with 11 sides. Use your conjecture from part b) to predict the sum of the interior angles of a polygon with 11 sides. Try this on your own first!!!!

Example 3b & c Determining a Formula for the Sum of the Interior Angles of a Triangle b) Based on the table, make a conjecture about the relationship between the sum of the measures of the interior angles and the number of sides of the polygon. Take number of sides and subtract 2 then multiply by 180 °. c) A Canadian loonie coin is an example of a polygon with 11 sides. Use your conjecture from part b) to predict the sum of the interior angles of a polygon with 11 sides.

Need to Know: By the triangle sum theorem, the sum of the interior angles of any triangle is 180 °. The sum of the measures of the interiors angles of a polygon with n sides is determined using. You’re ready! Try the homework from this section.