1. Triangles and Angles Sec 4.1 GOALS: To classify triangles by their angles and sides To find missing angle measures in triangles

2. B A Triangle – formed by three line segments that intersect only at their endpoints. C angle Triangle ABC Vertex B The line segments are,, and Side AC is opposite angle B Sides AB & CB are adjacent to vertex B

3. Angle and Side Classifications Triangles can be classified by their sides and angles. By sides  Scalene - no congruent sides  Equilateral - three congruent sides  Isosceles - at least two congruent sides

4. Angle and Side Classifications Triangles can be classified by their sides and angles.  By angles  Acute – an acute triangle is acute because it has three acute angles  Obtuse – an obtuse triangle is obtuse because it has one obtuse angle  Right – a right triangle is right because it has one right angle  Equiangular – an equiangular triangle has three congruent sides

5. Lets classify some triangles Notice: All triangles have at least two acute angles so they are classified by the measure of the third angle.

6. Special triangles Right TriangleIsosceles Triangle Can you have an isosceles right triangle? (the base would be the hypotenuse) Leg “b” Leg “a” Hypotenuse “c” Leg base

7. Triangle Sum Theorem The sum of the measures of the angles in a triangle is 180 degrees If x = 55, and y = 75, then z = 180 – (55+75) = 50

8. Exterior Angles of a Triangle Exterior angles are angles that are adjacent to the interior angles in a triangle. There are 6 in total, 3 pairs of congruent angles. It is customary to only talk about one exterior angle at each vertex.

9. Exterior Angles Theorem The measure of an exterior angle is equal to the sum of the two remote interior angles. If x = 35 degrees and y = 45 degrees, then the measure of angle 1 is equal to 80.

10. Corollary A corollary to a theorem is a statement that can be proved easily using a theorem. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary.

11. You Try! Find the missing angle measure and classify each triangle

12. Examples Find x or y.