(edited, original ppt by T.Carl)

1. TRIANGLES

3. Thesegments are called the sides.vertex side side vertex vertex side

4. Naming a Triangle and its parts Triangle ABC / ΔABC Angles: A, B, & C Sides: AB, BC, & CA a, b, & c B c a A C b Note: Naming = Consecutive vertices (preferably clockwise)

5. Triangle Classification (accdg. to sides) ISOSCELES At least 2 sides congruent SCALENE No sides congruent EQUILATERAL All sides congruent Using the Geoboards

6. Triangle Classification (accdg. to angles) ACUTE 3 acute angles RIGHT 1 right angle ┌ EQUIANGULAR All angles congruent OBTUSE 1 obtuse angle

7. Paper-folding Investigation B Draw a triangle similar in shape to the ΔABC. Cut it out. Slide point A along AC toward point C until the fold passes through point B. The crease intersects AC at point D. Unfold the triangle. A C B C D A B A C D

9. Bring points B and C to point D and crease.B A C D B A C D What appears to be true about the sum of the measures of these angles three angles?

10. The sum of the measures of angles of a triangle is 180o. B 4 5 3 B A C 1 2 A C A + B + C = 180o

11. Sample Problems The angles of a triangle are in a ratio 3:4:5. Find the measures of all the angles. 2. (2x)o (4x-8)o (5x-10)o

12. TRUE or FALSE? If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent. Each angle of an equiangular triangle measures 60o. In a triangle, there can be at most one right triangle, or at most one obtuse angle. The acute angles of a right triangle are complementary.

13. Exterior Angles of a Triangle ΔABC has been extended to form exterior angles: 1, 2, & 3. Each exterior angle has an adjacent interior angle and two remote interior angles. Example: Exterior angle: Adjacent interior angle: Two remote angles: A 1 6 3 4 5 B C 2 2 4 6 & 5

14. Sample Problems: Solve for x. 1. 2. 40o xo 23o 84o 7xo 5xo