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Review Sheet # 5 NAME_______________________________________DATE_______________PER._______ REVIEW SHEET # 5: ANGLES OF POLYGONS PART 1. IMPORTANT GEOMETRIC TERMS Write a thorough definition for each of the following geometric terms. A figure formed by the segments determined by 3 non1. ___________________________ collinear points. A triangle with no two sides congruent. 2. _ Scalene Triangle_________ A triangle with at least two sides congruent. 3. ___________________________ A triangle with all sides congruent. 4. ____Equilateral Triangle______ A triangle in which all of the angles are acute. 5. ___________________________ A triangle with an obtuse angle. 6. ____Obtuse Triangle______ A triangle with a right angle. 7. ___________________________ A triangle with all angles congruent. 8. ___________________________ 9. ______Polygon_____________ A closed figure formed by three or more segments intersecting at their endpoints. PART 2. TRIANGLE BASICS Decide if the following lengths can be sides of a triangle. If yes, classify the triangles by SIDES. 10. YES or NO (18 is NOT bigger than 20) 8, 10, 20 Classification:___none__________________ 11. YES or NO 10, 11, 14 Classification:_________________________ 12. YES or NO Classification:_________________________ 10, 10, 10 Review Sheet # 5 Pg. 2 The measures of two angles of a triangle are given. Find the measure of the third angle, then classify the triangle by ANGLES. 13. Third Angle = ___90_________ 57, 33 Classification:______Right Triangle________ 14. Third Angle = ____________ 36, 52 Classification:_________________________ 15. Third Angle = ____________ 50, 50 Classification:_________________________ Choose the best answer for each of the following. ___D__16. Which of the following CANNOT be the length of the third side? A. B. C. D. ______17. 4 5 6 7 (3+4 = 7; must be GREATER THAN 7) 3 4 Which of the following CANNOT be the length of the third side. A. B. C. D. 3 4 5 6 5 PART 3. ANGLES OF TRIANGLES Find the specified value(s). 18. x = ___69____ 2 x + 21 + 90 = 180 x + 111= 180 x 21 19. y = __________ 100 y 160 Review Sheet # 5 Pg. 3 ADD UP ALL x’s and set it equal to 180 E 20. x = __________ m E = __________ 2x x F D x ADD THE 2 INSIDE ANGLES AND SET IT EQUAL TO OUTSIDE ANGLE B 80 21. x = __________ m C = _________ m ABC = __________ A x (2x – 4) C Answer each of the following. In ABC, AB = 6, BC = 8, and AC = 12. List the angles of ABC in order from largest to smallest. 22. Angles: < B, < A, < C **DRAW the Triangle** In XYZ, mX = 103, mY = 41, and mZ = 36. List the sides of XYZ in order from shortest to longest. 23. Sides: PART 4. POLYGONS AND THEIR ANGLES Classify each of the following polygons, then determine if it is convex or concave. 24. 25. Classification:____________________ CONVEX or CONCAVE? Classification:____________________ CONVEX or CONCAVE? Review Sheet # 5 Pg. 4 Find the following. ___1440_______26. Find the sum of the measures of the interior angles of a decagon. 180(n- 2)= 180 (10 – 8) = 180 (8) = 1440 _______________27. Find the sum of the measures of the interior angles of an undecagon. _______________28. Find the measure of one interior angle of a regular undecagon. ____156______29. Find the measure of one interior angle of a regular polygon with 15 sides. One interior angle = 180 (n- 2)/ n = 180 (15- 2)/15 = 180(13)/15 = 2340/15 _______________30. Find the number of sides of a regular polygon, if each interior angle has a measure of 162 _______________31. The sum of the measures of the interior angles of a polygon is 900. Find the number of sides of the polygon. Review Sheet #5 Pg. 5 _______________32. Find the sum of the exterior angles of a 32-gon. _______________33. Find the measure of one exterior angle of a regular polygon with 14 sides. _____16_______34. Find the number of sides of a regular polygon if each exterior angle has a measure of 22.5. n = 360/ exterior angle = 360/22.5 = 16 PART 5. REVIEW For each of the following pairs of angles, tell what type of pair they are, and tell whether each pair is congruent or supplementary. 1 2 4 3 6 5 8 7 ANGLE PAIR 35. 1 and 6 36. 2 and 7 37. 5 and 3 38. 4 and 8 39. 1 and 7 TYPE CORRESPONDING or SUPPLEMENTS? CONGRUENT