Triangles and Angles

Classifying Triangles Line segments are congruent if they have the same length; shown by the number of marks on the line segment One way to classify triangles is by the number of congruent sides they have Congruent

Classifying Triangles Scalene Triangles have no congruent sides Isosceles Triangles have two congruent sides Equilateral Triangles have three congruent sides

Classifying Triangles Another way to classify triangles is by the measure of their angles Acute Triangles have three acute angles Obtuse Triangles have one obtuse angle Right Triangles have one right angle

Classifying Triangles Checkpoint Classify each triangle by its sides and it’s angles: Angle: Angle: Angle: Side: Side: Side: Acute Equilateral Obtuse Scalene Right Isosceles

Triangle Mini-Lab Materials Needed: Pencil Ruler (share with a neighbor) Scissors (share with a neighbor)

Triangle Mini-Lab Using a ruler and pencil, draw any large triangle and cut it out with scissors. Individually label each angle 1, 2, and 3. Tear off (do NOT cut) a large section of each angle and arrange so each vertex is touching and each angle is adjacent to the next.

Triangle Mini-Lab What type of angle did the three angles form when placed together? What is the measure of this angle? Let’s confirm…. A straight angle 180º

Interior Angles of a Triangle The sum of the measures of the angles of a triangle is 180

Finding The Measures of Angles Checkpoint Find the measure of each angle then classify the triangle by its angles: m a = 46º, m b = 42º, m c = Classify: xº + 46º + 42º = 180º xº + 88º = 180º x = 92º 92º Obtuse

Finding The Measures of Angles Checkpoint Find the measure of each angle then classify the triangle by its angles: m a = 3xº, m b = 2xº, m c = xº Classify: xº + 2xº + 3xº = 180º 6xº = 180º x = 30º 3(30º) = 90º 2(30º) = 60º x = 30º Right

Finding The Measures of Angles Checkpoint Find the measure of each angle then classify the triangle by its angles: m a = 4xº, m b = 3xº, m c = 2xº Classify: 4xº + 3xº + 2xº = 180º 9xº = 180º x = 20º 4(20º) = 80º 3(20º) = 60º 2(20º) = 40º Acute

Finding The Measures of Angles Checkpoint Find the measure of each angle a° b° c ° 65 ° 70 ° bº + 70º + 65º = 180º bº + 135º = 180º b = 45º c is alternate interior with 65° c = 65° a is alternate interior with 70° a = 70°

Finding The Measures of Angles Checkpoint Find the measure of each angle a is alternate interior with 123° a = 123° bº + 123º + 35º = 180º bº + 158º = 180º b = 22º 123° a° b° 35° c° c is alternate interior with 35° c = 35°

Homework Skill 6: Triangles (both sides) 6-2 Practice Skills: Triangles and Angles (both sides) Due Tomorrow!