1. Pre-Algebra Homework Page 248 #1-9

2. NEW! Student Learning Goal Chart Lesson Reflection for Chapter 5

3. Pre-Algebra Learning Goal Students will understand plane geometry through plane figures and patterns in geometry.

4. Students will understand plane geometry through plane figures and patterns in geometry by completing the following: Learn to classify and name figures (5-1) Learn to identify parallel and perpendicular lines and the angles formed by a transversal (5-2) Learn to find unknown angles in triangles (5-3)

5. Hop On Board the Fast Track Train! Chapter 5 Sections 1 & 2

6. 5-1 Points, Lines, Planes, and Angles Learning Goal Assignment Learn to classify and name figures.

7. A right angle measures 90°. An acute angle measures less than 90°. An obtuse angle measures greater than 90° and less than 180°. Complementary angles have measures that add to 90°. Supplementary angles have measures that add to 180°. 5-1 Important Notes

8. Congruent figures have the same size and shape. Segments that have the same length are congruent. Angles that have the same measure are congruent. The symbol for congruence is , which is read “is congruent to.” Intersecting lines form two pairs of vertical angles. Vertical angles are always congruent, as shown in the next example. 5-1 Important Notes

9. 5-1 FAST TRACK Quiz In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. 1. Name three points in the figure. 3. Name a right angle in the figure. 4. Name a pair of complementary angles. 5. If m1 47°, then find m3. 2. Name two lines in the figure. Possible answer: A, B, and C Possible answer: AGF Possible answer: 1 and 2 47° Possible answer: AD and BE

10. 5-2 Parallel and Perpendicular Lines Learning Goal Assignment Learn to identify parallel and perpendicular lines and the angles formed by a transversal.

11. Parallel lines are two lines in a plane that never meet, like a set of perfectly straight, infinite train tracks. Perpendicular lines are lines that intersect to form 90° angles. 5-2 Important Notes

12. PROPERTIES OF TRANSVERSALS TO PARALLEL LINES If two parallel lines are intersected by a transversal, the acute angles that are formed are all congruent, the obtuse angles are all congruent, and any acute angle is supplementary to any obtuse angle. If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90° angles. 5-2 Important Notes

13. If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines. 5-2 Important Notes

14. 5-2 FAST TRACK Quiz In the figure a || b. 1. Name the angles congruent to 3. 2. Name all the angles supplementary to 6. 3. If m1 = 105° what is m3? 4. If m5 = 120° what is m2? 1, 5, 7 1, 3, 5, 7 105° 60°

15. 5-3 Triangles Learning Goal Assignment Learn to find unknown angles in triangles.

16. Pre-Algebra 5-3 Triangles Vocabulary Triangle Sum Theorem acute triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle

17. Pre-Algebra 5-3 Triangles If you tear off two corners of a triangle and place them next to the third corner, the three angles seem to form a straight line.

18. Pre-Algebra 5-3 Triangles Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown. The three angles in the triangle can be arranged to form a straight line or 180°. The sides of the triangle are transversals to the parallel lines.

19. Pre-Algebra 5-3 Triangles An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

20. Pre-Algebra 5-3 Triangles Additional Example 1A: Finding Angles in Acute, Right and Obtuse Triangles Find p in the acute triangle. 73° + 44° + p = 180° 117° + p = 180° P = 63° –117°

21. Pre-Algebra 5-3 Triangles Try This: Example 1A Find a in the acute triangle. 88° + 38° + a = 180° 126° + a = 180° a = 54° –126° 88° 38° a°a°

22. Pre-Algebra 5-3 Triangles Additional Example 1B: Finding Angles in Acute, Right, and Obtuse Triangles Find c in the right triangle. 42° + 90° + c = 180° 132° + c = 180° c = 48° –132°

23. Pre-Algebra 5-3 Triangles Find b in the right triangle. 38° + 90° + b = 180° 128° + b = 180° b = 52° –128° 38° b°b° Try This: Example 1B

24. Pre-Algebra 5-3 Triangles Additional Example 1C: Finding Angles in Acute, Right, and Obtuse Triangles Find m in the obtuse triangle. 23° + 62° + m = 180° 85° + m = 180° m = 95° –85° –85°

25. Pre-Algebra 5-3 Triangles Find c in the obtuse triangle. 24° + 38° + c = 180° 62° + c = 180° c = 118° –62° –62° c°c° 24° 38° Try This: Example 1C

26. Pre-Algebra 5-3 Triangles An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

27. Pre-Algebra 5-3 Triangles Additional Example 2A: Finding Angles in Equilateral, Isosceles, and Scalene Triangles Find angle measures in the equilateral triangle. 3b° = 180° b° = 60° 3b° 180° 3 = Triangle Sum Theorem All three angles measure 60°. Divide both sides by 3.

28. Pre-Algebra 5-3 Triangles Try This: Example 2A 39° + t° + t° = 180° 39° + 2t° = 180° 2t° = 141° –39° –39° Find angle measures in the isosceles triangle. 2t° = 141° 2 t° = 70.5° Triangle Sum Theorem Combine like terms. Subtract 39° from both sides. Divide both sides by 2 t° 39° The angles labeled t° measure 70.5°.

29. Pre-Algebra 5-3 Triangles Additional Example 2B: Finding Angles in Equilateral, Isosceles, and Scalene Triangles 62° + t° + t° = 180° 62° + 2t° = 180° 2t° = 118° –62° –62° Find angle measures in the isosceles triangle. 2t° = 118° 2 t° = 59° Triangle Sum Theorem Combine like terms. Subtract 62° from both sides. Divide both sides by 2. The angles labeled t° measure 59°.

30. Pre-Algebra 5-3 Triangles 3x° + 7x° + 10x° = 180° 20x° = 180° x = 9° 20 20 Find angle measures in the scalene triangle. Triangle Sum Theorem Combine like terms. Divide both sides by 20. 3x°3x°7x°7x° 10x° Try This: Example 2B The angle labeled 3x° measures 3(9°) = 27°, the angle labeled 7x° measures 7(9°) = 63°, and the angle labeled 10x° measures 10(9°) = 90°.

31. Pre-Algebra 5-3 Triangles Additional Example 2C: Finding Angles in Equilateral, Isosceles, and Scalene Triangles 2x° + 3x° + 5x° = 180° 10x° = 180° x = 18° 10 10 Find angle measures in the scalene triangle. Triangle Sum Theorem Combine like terms. Divide both sides by 10. The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

32. Pre-Algebra 5-3 Triangles Find angle measures in the equilateral triangle. 3x° = 180° x° = 60° 3x° 180° 3 = Triangle Sum Theorem All three angles measure 60°. Try This: Example 2C x°x° x°x° x°x°

33. Pre-Algebra 5-3 Triangles The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible picture. Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle measure. 1212 Additional Example 3: Finding Angles in a Triangle that Meets Given Conditions

34. Pre-Algebra 5-3 Triangles Additional Example 3 Continued x° + 6x° + 3x° = 180° 10x° = 180° 10 10 x° = 18° Triangle Sum Theorem Combine like terms. Divide both sides by 10. Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 1212

35. Pre-Algebra 5-3 Triangles X° = 18° x° = 18° 6 18° = 108° 3 18° = 54° The angles measure 18°, 54°, and 108°. The triangle is an obtuse scalene triangle. Additional Example 3 Continued Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 1212

36. Pre-Algebra 5-3 Triangles Lesson Quiz: Part 1 1. Find the missing angle measure in the acute triangle shown. 2. Find the missing angle measure in the right triangle shown. 38° 55°

37. Pre-Algebra 5-3 Triangles Lesson Quiz: Part 2 3. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°. 4. Find the missing angle measure in an obtuse triangle with angle measures of 10° and 15°. 50° 155°