4 2 Classifying Triangles Rigor Classify triangles by
4 -2 Classifying Triangles Rigor • Classify triangles by their angle measures and side lengths. • Use triangle classification to find angle measures and side lengths. Holt Mc. Dougal Geometry
4 -2 Classifying Triangles Review By side lengths • Scalene – no sides congruent • Isosceles – at least 2 sides congruent • Equilateral – all 3 sides congruent By angle measures • Acute – all 3 angles 0 o < x < 90 o • Obtuse – 1 angle 90 o < x < 180 o • Right – 1 angle is 90 o • Equiangular – all angles are congruent Remember! When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent. Holt Mc. Dougal Geometry
4 -2 Classifying Triangles Example 1: Classify BDC, BDA, and angle measures. Holt Mc. Dougal Geometry ADC by their
4 -2 Classifying Triangles Example 2: Find the side lengths of isosceles JKL and equilateral FGH. Holt Mc. Dougal Geometry
4 -2 Classifying Triangles Example 3: Application A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the triangle is 18 feet long. How many triangles can be formed from 420 feet of steel beam? Holt Mc. Dougal Geometry
4 -2 Classifying Triangles Workbook Examples: Use Pythagorean Theorem to Classify Triangles • Complete example 1 on page 137 • Highlight formulas at the bottom of page 137 • Complete example 2 on page 138 Holt Mc. Dougal Geometry
4 -2 Classifying Triangles You Try! • Workbook Page 138 Practice Problems #1 & 3 • CHANGE DIRECTIONS: Classify triangles by sides AND angles. • You don’t need to calculate perimeter • You must use Pythagorean theorem to justify your answer. Holt Mc. Dougal Geometry
4 -2 Classifying Triangles 4 -2 Honors Assignments • Primary Assignment: join. quizizz. com • Codes: – Period 1: 265493 Due Monday – Period 5: 710672 Due Monday – Period 6: 161134 Due Wednesday • Secondary Assignment: – Textbook pg 227 -228 #9 – 19, 33, 34 Holt Mc. Dougal Geometry
4 -2 Classifying Triangles 4 -2 Standard Assignments • Primary Assignment: join. quizizz. com • Codes: – Period 2: 386851 Due Tuesday – Period 4: 443808 Due Tuesday – Period 7: 136775 Due Tuesday • Secondary Assignment: – Textbook pg 227 -228 #9 – 19, 32, 34 Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles Rigor • Find the measures of interior and exterior angles of triangles. • Apply theorems about the interior and exterior angles of triangles. Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles Highlight this theorem and complete the proof in your workbook on page 142. Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles Example 4: Find m XYZ, m YWZ, and m YXW. Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles Example 5: Astronomy An asterism is a group of stars that is easier to recognize than a constellation. The Summer Triangle is composed of the stars Deneb, Altair, and Vega. What is the measure of each angle in the Summer Triangle? Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem. Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles Example 6 The measure of one of the acute angles in a right triangle is 63. 7°. What is the measure of the other acute angle? Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles Interior Angle Sum Theorem Divide the polygons into triangles and use the Triangle Angle Sum Theorem to calculate the sum of the interior angles of the polygons. What equation could be used to calculate the sum of any polygon’s interior angles, given the number of sides n? Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles • Read and Highlight important information on workbook page 143, including remote interior angles and the Exterior Angles Theorem. • We will prove the Exterior Angles Theorem together Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles Example 7: Find m B Holt Mc. Dougal Geometry Find m ACD
4 -3 Angle Relationships in Triangles Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles Example 8: Find m P. Holt Mc. Dougal Geometry
4 -3 Angle Relationships in Triangles 4 -3 Assignments • Primary assignment: – Workbook page 145 #2, 5 – 9, 12 (Honors also #4 & 11); page 146 #1 – 4, 7 – 9 – Due Wednesday for all classes • Secondary assignment: – Textbook pg 236 #15 – 23, 26 Holt Mc. Dougal Geometry
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