Triangles and Angles

Classifying Triangles Line segments are congruent if they have the same length One way to classify triangles is by the number of congruent sides they have

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 angle by it’s sides and it’s angles: Angle: Angle: Angle: Side: Side: Side: Acute Equilateral Obtuse Scalene Right Isosceles

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

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

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 180 degrees

Triangle Mini-Lab Flip over one angle and use your protractor to measure it. Write the measure on the back of the angle and repeat these steps for the other two angles. Add up the measures of each of the angles.

Finding The Measures of Angles In an equilateral triangle, all of the sides are congruent and all of the angle measurements are congruent What is the measure of each angle?

Finding The Measures of Angles What do we know? We know that each angle is congruent but we don’t know their measure. Let’s call it “X.” We know that all three angles add up to 180 degrees. Therefore, X + X + X = 180 What is the measure of each angle? 3x = 180 X = 60

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

Finding The Measures of Angles Checkpoint Find the measure of each triangle then classify the triangle by it’s angles: m a = 3x, m b = 2x, m c = x Classify: 3 x 30 = 90 2 x 30 = 60 x = 30 x + 2x + 3x = 180 6x = 180 x = 30 Right

Finding The Measures of Angles Checkpoint Find the measure of each triangle then classify the triangle by it’s angles: m a = 4x, m b = 3x, m c = 2x Classify: 4 x 20 = 80 3 x 20 = 60 2 x 20 = 40 4x + 3x + 2x = 180 9x = 180 x = 20 Acute

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