Download 4.1 Classify Triangles

Geometry Chapter 4: Congruent Triangles 4.1-­‐ Apply Triangle Sum Properties SWBAT: classify triangles and find measures of their angles. Common Core: G.CO.10
Geometry Chapter 4: Congruent Triangles Example 1: Classify triangles by sides and angles Classify the triangle by measuring its sides and angles. Example 2: Classify a triangle in the coordinate plane Classify ∆𝑅𝑆𝑇 by its sides. Then determine if the triangle is a right triangle. Geometry Chapter 4: Congruent Triangles v Polygons have two types of angles: Interior and Exterior Interior angles are inside of the polygon. To form exterior angles we must extend the sides of our polygons. Theorem 4.1: Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is __________________. Prove the Triangle Sum Theorem Given: ∆𝐴𝐵𝐶 Prove: 𝑚∠1 + 𝑚∠2 + 𝑚∠3 = 180° (Hint: draw an auxilary line) Geometry Chapter 4: Congruent Triangles Theorem 4.2: Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two _____________________________________________ angles. Example 3: Find an angle measure a) Find 𝑚∠𝐽𝐾𝑀 b) Find 𝑚∠𝐷𝐶𝐵 Corollary to the Triangle Sum Theorem The acute angles of a right triangle are _______________________________________. Geometry Chapter 4: Congruent Triangles Example 4: Find angle measures from a verbal description Ramps The front face of the wheelchair ramp shown forms a right triangle. The measure of one acute angle in the triangle is seven times the measure of the other. Find the measure of each acute angle. Extra Practice: 1) Find the measure of ∠1 in the figure at the right. 2) Find the measures of each interior angle in ∆𝐴𝐵𝐶, 𝑤ℎ𝑒𝑟𝑒 𝑚∠𝐴 = 𝑥°, 𝑚∠𝐵 = 2𝑥°, 𝑚∠𝐶 = 3𝑥°. 3) Find the measures of the acute angles of the right triangle in the diagram at the right. Homework: Pgs. 221 – 222 #’s 1 – 10 All, 13 – 27 All, 33, 35