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Honors Geometry Chapter 1 Review True/False 1. _____ AD ≅ DE ≅ EC 2. _____m∠DBE = 30° 3. _____m∠ABE = 2(m ∠EBC) C B E D A Always/Sometimes/Never 4. _____A line has a bisector. 5. _____A false statement has a false converse. 6. _____An angle whose measure is between 0° and 90° is an acute angle. 7. _____The sum of two acute angles is an acute angle. Fill in the blanks. 8. uuur uuur _____ AD ∩ EA 9. uuur uuur _____DA ∪ DB 10. suur suur _____ AD ∩ BC 11. _____∠ABE ∩ ∠EBC 12. _____The number of angles that have their vertex at point B. 13. _____If three of the five labeled points are chosen at random, what is the probability that they form a triangle? Use the following logical sentences for both parts of question 14. 14. You are an honors geometry student and therefore you want to get an A on this test. If you don’t know the material in Chapter 1, you won’t get an A on this test. a.) Write the first sentence in if ⇒ then form. b.) What can you conclude? 15. Write the sentence in if ⇒ then form. All obtuse triangles have exactly one obtuse angle and two acute angles. 16. Write the converse of this statement. If a number is divisible by six, then it is divisible by three. 17. Find the angle between the hands of a clock at 11:35. 12 11 1 2 10 3 9 4 8 5 7 18. Change 33’20’’ to degrees. 19. ∠ABC is a right angle. Find m∠ABD. 6 A D B 20. ∠2 is five times as large as ∠1. Find m∠2. 10° 35' 10'' C 2 1 21. P uuur QS bisects ∠PQR. Solve for y in terms of x. Q S (5 x-6) ° (x-2y)° R 22. If ST = 4, SE = 11, ET = 7, and S, T, and E are collinear, then point _____ is between the other two points. Justify your answer with a diagram. 23. The sides of a triangle are in the ratio 4:5:7 and the perimeter of the triangle is 72. Find the length of the shortest side. 24. Given: EB and EC trisect AD AB = 7x+3 AC = 11y-7 CD = 8x+2y-10 A Find: B E AD C D 25. In the figure, is ∠QPS ACUTE, RIGHT, or OBTUSE? Write a paragraph proof to justify your answer. P (2 x+10) ° (x+25)° (3 x)° Q (5 x-20) ° R S 26. A triangle has sides 3 cm and 11 cm. What are the restrictions on the length of the third side? 27. Subtract. 90° - 30° 52’ 20’’. 28. Given: m ∠AXB = 70° m ∠BXY = 20° ∠Y is a right angle A B Prove: ∠AXY ≅ ∠Y X Y Honors Geometry Chapter 1 Review – Answer Key 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. False False True Never Sometimes Always Sometimes EA ∠BDA C 11. 12. BE 6 3 5 a.) b.) 13. 14. If you are an honors geometry student, then you want to get an A on the test. If you are an honors geometry student, then you know the material. OR If you don’t know the material, then you are not an honors geometry student. 15. If a triangle is an obtuse triangle, then it has exactly one obtuse angle and two acute angles. 16. If a number is divisible by three, then it is divisible by six. 17. 137.5° or 137°30’ 18. 5 ° 9 19. 79° 24’ 50’’ 28. 20. 150° Statements Reasons 21. y = -2x + 3 or y = 3 – 2x 1. given 22. T 1. m ∠AXB = 70° m ∠BXY = 20° ∠Y is a right angle 23. 18 units 2. m ∠AXY = 90° 2. addition 24. x = 3, y = 5, AD = 72 3. m ∠Y = 90° 3. right ∠ = 90° 25. ∠QPS is obtuse (m ∠QPS = 110°) 4. ∠AXY ≅ ∠Y 4. 2 ∠s with = measures are ≅ 26. 8 < x < 14 27. 59° 7’ 40’’