Bellwork What are the coordinates of the point P that partitions the directed segment from C(1, - 6) to D(9, 6) in a 1 to 3 ratio? What is always the first reason in a proof? What word can NEVER be a reason in proof, even though it appears in the proof’s setup?

Rigor Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths.

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 0o < x < 90o Obtuse – 1 angle 90o < x < 180o Right – 1 angle is 90o Remember! When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent.

Example 1: Classify BDC, BDA, and ADC by their angle measures.

Example 2: Find the side lengths of isosceles JKL and equilateral FGH.

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?

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

Standard: 4-2 Assignment from the Workbook Page 138 Practice Problems #1-4 CHANGE DIRECTIONS: Classify triangles by sides AND angles. You don’t need to calculate perimeter You must use Pythagorean theorem to justify your answer. Page 139 #1 – 7 Page 140 #1, 2, 5

Honors: 4-2 Assignment from the Workbook Page 138 Practice Problems #1-4 CHANGE DIRECTIONS: Classify triangles by sides AND angles. You don’t need to calculate perimeter You must use Pythagorean theorem to justify your answer. Page 139 #3 – 8 Page 140 ALL

Rigor Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles.

Triangle Exploration Use a straight edge to draw 3 triangles on scratch paper: one acute, one obtuse, and one right. Follow the investigation instructions on workbook page 141 Answer reflection questions 1a – 1d. Be ready to discuss answers in a few minutes.

Highlight this theorem in your workbook on page 142.

Example 1: Find mXYZ, mYWZ, and mYXW.

Example 1b: 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?

A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

Example 2 The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

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?

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

Example 3: Find mB Find mACD

Example 4: Find mP.

4-3 Assignment from the Workbook Page 145 #2, 5 – 9, 12 (Honors also #4 & 11) Page 146 #1 – 4, 7 – 9