1. Activity You can find the sum of the angle measures in a triangle. Triangles 10 3. 1 Cut a triangle from the corner of a piece of paper. Label the corners  A,  B, and  C. Rearrange  A,  B, and  C so that they are adjacent. Then make a conclusion about the angles of the triangle. 2 3 Tear the corners off the triangle. A B C A B C C B AA C B C B A In the activity, you found that the sum of the angle measurements in ABC is 180º. The sum of the angle measurements in any triangle is 180º.

2. Triangles 10 3. 83º 26º x ºx º Sum of angle measures in a triangle is 180º. x º + 83º + 26º = 180º x + 109 = 180 x = 71 Add 83 and 26. ANSWER The value of x is 71. Subtract 109 from each side. EXAMPLE 1 Finding an Angle Measure in a Triangle Find the value of x in the triangle shown.

3. Triangles Interior and Exterior Angles The three angles of any triangle are called interior angles. interior angles exterior angle 10 3. The sides of a triangle can be extended to form angles outside of the triangle that are adjacent and supplementary to the interior angles. These angles are called exterior angles. You can use the measures of interior angles to find the measures of exterior angles.

4. Triangles Finding the Measure of an Exterior Angle EXAMPLE 2 Find the value of y in the figure. 10 3. Definition of supplementary angles y º + 35º = 180º y = 145 ANSWER The value of y is 145. Subtract 35 from each side. To find the value of y, use the fact that adjacent interior and exterior angles of a triangle are supplementary. 55º 35º yºyº

5. Triangles NOTE BOOK Acute Triangle An acute triangle has three acute angles. Classifying Triangles by Angle Measures 10 3. You can classify any triangle by the measures of its interior angles. Obtuse TriangleRight Triangle A right triangle has one right angle. An obtuse triangle has one obtuse angle. 50º 40º 35º 120º 25º 70º 60º 50º

6. Triangles 10 3. Congruent Sides Just as congruent angles have the same measure, congruent sides of a triangle have the same length. X ZY You can use special marks to indicate that two sides or two angles of a triangle are congruent. In the triangle above, the marks show that XY  XZ and that  Y   Z. You can classify any triangle by the lengths of its sides.

7. Triangles NOTE BOOK Equilateral Triangle An equilateral triangle has 3 congruent sides. Classifying Triangles by Side Lengths 10 3. Scalene Triangle Isosceles Triangle An isosceles triangle has at least 2 congruent sides. A scalene triangle has no congruent sides. 14 ft 11 ft 5 ft 8 m 5 m 9 in.

8. Triangles Classifying a Triangle by Angle Measures EXAMPLE 3 Classify the triangle formed by the plant hanger by its angle measures. 10 3. The triangle has one right angle, so it is a right triangle.

9. Triangles Classifying a Triangle by Angle Measures EXAMPLE 3 Classify the triangle formed by the plant hanger by its angle measures. 10 3. The triangle has one right angle, so it is a right triangle. Classifying a Triangle by Side Lengths EXAMPLE 4 Classify the triangle by the lengths of its sides. All three sides of the triangle are congruent, so the triangle is both isosceles and equilateral. 36 in.