4.1+Triangles+&+Angles


 * __Summary__**
 * Classifying Triangles and Angles
 * Measuring Angles in Triangles
 * Applying the Triangle Sum Theorem and the exterior angle theorem to find the measures of angles of the triangle

(pg. 196)
 * __Vocab.__**
 * Triangle:** a figure formed by 3 segments joining 3 non-collinear points
 * Vertex:** 3 points joining the side of a triangle is a vertex
 * Adjacent Sides:** 2 sides sharing a common vertex and adjacent side
 * Legs:** the sides that form the right angle are the legs of the angle
 * Hypotenuse:** the side opposite the right angle is the hypotenuse
 * Base:** Isosceles triangle with 2 congruent sides, the 3rd side is the base
 * Corollary:** A corollary to a theorem
 * Interior Angles:** When the sides of a triangle are extended, they are the 3 original angles
 * Exterior Angles:** When the sides of a triangle are extended the interior angles
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/mcd_ma_geo_lsn_0395937779_p194_f13.gif align="top"]]

__Theorems__**
 * Corollary to the Triangle Sum Theorem:** The acute angle of a right triangle are complementary
 * Triangle Sum Theorem:** The sum of the interior angles of a triangle is 180°. //m//[[image:http://images.classwell.com/ebooks/images/mcd_geo/angle.gif align="absmiddle"]]//A// + //m//[[image:http://images.classwell.com/ebooks/images/mcd_geo/angle.gif align="absmiddle"]]//B// + //m//[[image:http://images.classwell.com/ebooks/images/mcd_geo/angle.gif align="absmiddle"]]//C// = 180° (pg. 196)

[] [|http://www.mathwarehouse.com/geometry/triangles/index.php]
 * __Websites__**


 * __Practice Problems:__**
 * 1.** Δ//ABC// has three acute angles and no congruent sides. It is an acute scalene triangle. (Δ//ABC// is read as “triangle //ABC//.”) **pg. 194**




 * 2.** What are the other two angle measures? **pg.194**




 * Answer:** 25


 * 3. The diagram shows a triangular loom. Explain why Δ//ABC// is an isosceles right triangle. pg. 195

Answer:** 
 * In the diagram, you are given that [[image:http://images.classwell.com/ebooks/images/mcd_geo/angle.gif align="absmiddle"]]//C// is a right angle. By definition, Δ//ABC// is a right triangle. Because //AC// = 5 ft and //BC// = 5 ft, [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_ac.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/congruent.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_bc.gif align="absmiddle"]]. By definition, Δ//ABC// is also an isosceles triangle. ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif height="11"]] ||