4-1+Triangles+and+Angles

TRIANGLES & ANGLES

In section 4-1, you will be reviewing how to classify triangles by their sides and angles and how to find angle measures in triangles. To look back at the textbook for more review, you can go to pages 194-201.

**Helpful Websites: ** http://www.winpossible.com/lessons/Geometry_Triangle_Angle-Sum_Theorem.html http://www.cliffsnotes.com/study_guide/Exterior-Angle-of-a-Triangle.topicArticleId-18851,articleId-18784.html

**__Vocabulary : __** Triangle -  a plane figure with 3 sides and 3 angles Vertex - each of the 3 points joining the sides of a triangle  Adjacent sides - 2 sides sharing a common vertex  Legs - the 2 sides of a right triangle or an isosceles triangle  <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Base - <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;"> the third side of an isosceles triangle <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Hypotenuse - <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">the opposite side of the right triangle  <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Interior angles - <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">angles that are in between the 2 lines  <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Exterior angles - <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">angles that are on the outside of the 2 lines   <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Corollary - <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">acute angles of a right angle; a proof that is easily proven. **__<span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Theorems: __** <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Triangle Sum Thm - <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">the sum of the measures of the interior angles of a triangle is 180 ° <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Exterior Angle Thm - created when the sides of a triangle are extended. Each exterior angle is adjacent to one interior angle. (in the diagram, <1 is an exterior angle.) Exterior angles and adjacent interior angles form a linear pair. <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">﻿ <span style="color: #ff006d; font-family: Impact,Charcoal,sans-serif; font-size: 26px; line-height: 39px;"> <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">Corollary to the Triangle Sum Thm - <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">the acute angles of a right triangle are complementary. <span style="color: #000000; font-family: arial,helvetica,sans-serif;"> <span style="color: #ff006d; font-family: Impact,Charcoal,sans-serif; font-size: 26px; line-height: 39px;">

<span style="color: #ff006d; font-family: Impact,Charcoal,sans-serif; font-size: 150%;">Sample Problems <span style="color: #ff006d; font-family: Impact,Charcoal,sans-serif; font-size: 150%;">1) find x <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 150%;"> By using the exterior angle theorem, you can say: x = 35 + 100
 * x = 135**

<span style="color: #ff006d; font-family: Impact,Charcoal,sans-serif; font-size: 130%;">2) find x

<span style="color: #ff006d; font-family: Arial,Helvetica,sans-serif; font-size: 17px; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">

By using the Triangle Sum Thm, you can do: 35 + 23 + b = 180 58 + b = 180 b = 122 And by the Vertical Angles Theorem, you can that angle A = 122. Therefore, being able to use the Triangle Sum Theorem to do: 27 + 22 + x = 180 149 + x = 180
 * x = 31**

<span style="color: #000000; font-family: arial,helvetica,sans-serif;">**<span style="color: #ff006d; font-family: Impact,Charcoal,sans-serif; font-size: 17px; font-weight: normal; line-height: 25px;">Prove: <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 17px; font-weight: normal; line-height: 25px;">﻿m<1+m<2+m<3=180 **
 * <span style="color: #ff006d; font-family: Impact,Charcoal,sans-serif; font-size: 17px; font-weight: normal; line-height: 25px;">3) Given: ** ê <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">﻿ABC


 * <span style="color: #ff006d; font-family: Impact,Charcoal,sans-serif; font-size: 17px; font-weight: normal; line-height: 0px; overflow-x: hidden; overflow-y: hidden;">﻿ **[[image:treeees.png height="137"]]

<span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 150%;">**__PRACTICE!__** 1) Solve the following proof <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 150%;"> <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">2) Find the measure of the exterior angle <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;"> <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif;">3) Find the measure of the angles with a red number in them. <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 20px; line-height: 29px;"> <span style="color: #ff006d; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 20px; line-height: 29px;">** 4) Find the measure of angle LNM in this triangle. ** <span style="color: #000000; font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;">