Based on Chapter 5 of the textbook and Unit 5 of the study guide. For each of the following, write on the blank line the

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Based on Chapter 5 of the textbook and Unit 5 of the study guide. For each of the following, write on the blank line the letter of the word or phrase that best answers the question or completes the statement. 1. Which theorem compares two sides and the included angle of two triangles? (A) Hinge Theorem (B) Converse of the Hinge Theorem (C) Exterior Angle Inequality Theorem (D) Triangle Inequality Theorem 2. Name the longest side of ∠DEF. (A) DE (B) EF (C) DF (D) not enough information 3. What is the relationship between the lengths of DC and AD ? (A) DC<AD (B) DC>AD (C) DC=AD (D) not enough information 4. Carrie, Maria, and Nayla are friends that live close to one another. Which two friends have the shortest distance between them? (A) Maria and Nayla (B) Carrie and Maria (C) Carrie and Nayla (D) All three live equal distances from each other.
5. __ Name an altitude. (A) DE (C) GB (B) AB (D) CF 6. Name a perpendicular bisector. (A) DE (C) GB (B) AB (D) CF 7. Name an angle bisector. (A) DE (C) GB (B) AB (D) CF 8. _- Name a median. (A) DE (C) GB (B) AB (D) CF 9. Choose the assumption you would make to start an indirect proof. Given: ∠1 is an exterior angle of △ABC. Prove: ∠1=m∠B+m∠C (A) ∠1 is not an exterior angle of △ABC. (B) ∠1 is an interior angle of △ABC. (C) m∠1=m∠B+m∠C (S) m∠1=m∠B Which of the following sets of numbers can be the lengths of the sides of a triangle? (A) 12,9,4 (B) 1,2,3 (C) 5,5,10 (D) 2,5,18 Which assumption would you make to indirectly prove x>5 ? (A) x<5 (B) x≤5 (C) x=5 (D) x>5
Use the diagrams to answer questions 12 and 13. 12. - Given: AC≅DF,AB≅DE,m∠A>m∠D Which can be concluded by the Hinge Theorem? (A) △ABC≅△DEF (B) BC=EF (C) BC<EF (D) BC>EF 13. Given: AB≅DE,BC≅EF,AC<DF Which can be concluded by the Converse of the Hinge Theorem? (A) m∠B<m∠E (B) m∠B=m∠E (C) m∠B>m∠E (D) △BAC≅△EDF 14. If D is the circumcenter of △ABC and AD=6, find BD. (A) 4 (B) 6 (C) 9 (D) 12 15. Find the possible values for m∠1. (A) m∠1=124 (B) 90>m∠1>56 (C) 0<m∠1<56 (D) 180>m∠1>56
To receive full credit for the following questions, show as much work as possible. 16. Complete the proof below that utilizes the Triangle Inequality Theoram Given: PL∥MT K is the midpoint of PT Prove: PK+KM>PL Proof: 17. Write the assumption you would make to start an indirect proof of the following statements. A. If AB is an altitude of equilateral triangle ABC, then AB is a median. B. If n is an even number, then n2 is an even number. C. m∠ABC<m∠CBA
18. In △STR,H is the centroid, EH=6,DH=4, and SM=24. Find each measure. A. SH B. TH 19. Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. A. measures less than m∠1 B. measures less than m∠9 C. measures greater than m∠5 D. measures greater than m∠8
A. m∠APU B. AU C. m∠QPA D. m∠KQA 21. List the angles and sides of each triangle in order from smallest to largest. A. B. 1107 American School-Lansing II
22. Find the coordinates of the orthocenter of the triangle with the given vertices: P(−1,2),Q(5,2),R(2,1). 23. Compare the given measures using Theorems 5.12 or 5.13. A. m∠STR and m∠TRU B. PQ and RQ
24. Complete the indirect proof. Given: ∠1 a m∠2 and DG is not congruent to FG. Prove: DE is not congruent to FE. Assume that Assume the conclusion is false. EG≅EG△EDG≅△EFG This contradicts the given information, so the assumption must be Therefore, 25. Determine if it is possible to form a triangle with the given side lengths? Explain why or why not. A. 9 cm;10 cm;20 cm B. 15 km;17 km;19 km C. 2ft;3ft;4ft D. 14yd;17yd;31yd When you have completed the exam, fill in your name, student number, and other required information on each designated page of the exam and mail the exam to American School.