Geometry M1: Unit 3 Practice Exam

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Class: Date: Geometry M1: Unit 3 Practice Exam Short Answer 1. What is the value of x? 2. What is the value of x? 3. What is the value of x? 1

4. Find the value of x. The diagram is not to scale. Given: RS ST, m RST 5x 47, m STU 6x 5. Two sides of an equilateral triangle have lengths 2x 1 and 3x 2. Which could be the length of the third side: 10 x or 4x 3? 6. The legs of an isosceles triangle have lengths x 4 and 3x 18. The base has length x 6. What is the length of the base? 7. Find the values of x and y. 8. In an A-frame house, the two congruent sides extend from the ground to form a 34 angle at the peak. What angle does each side form with the ground? 9. Find the value of x. The diagram is not to scale. 2

10. Points B, D, and F are midpoints of the sides of ACE. EC = 41 and DF = 20. Find AC. The diagram is not to scale. 11. Find the value of x. 12. Find the value of x. The diagram is not to scale. 3

13. B is the midpoint of AC, D is the midpoint of CE, and AE = 25. Find BD. The diagram is not to scale. 14. Find the length of the midsegment. The diagram is not to scale. 15. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 4

16. Use the information in the diagram to determine the measure of the angle formed by the line from the point on the ground to the top of the building and the side of the building. The diagram is not to scale. 17. DF bisects EDG. Find the value of x. The diagram is not to scale. 18. Q is equidistant from the sides of TSR. Find m RST. The diagram is not to scale. 5

19. DF bisects EDG. Find FG. The diagram is not to scale. 20. Q is equidistant from the sides of TSR. Find the value of x. The diagram is not to scale. 21. Find the circumcenter of the triangle. 22. Find the circumcenter of EFG with E(4, 4), F(4, 0), and G(6, 0). 6

23. Find the length of AB, given that DB is a median of the triangle and AC = 22. 24. In ACE, G is the centroid and BE = 21. Find BG and GE. 25. In ABC, centroid D is on median AM. AD x 5 and DM 2x 4. Find AM. 26. Name a median for PQR. 7

27. What is the name of the segment inside the large triangle? 28. Name the second largest of the four angles named in the figure (not drawn to scale) if the side included by 1 and 2 is 13 cm, the side included by 2 and 3 is 8 cm, and the side included by 3 and 1 is 15 cm. 29. m A 9x 7, m B 7x 9, and m C 28 2x. List the sides of ABC in order from shortest to longest. 30. List the sides in order from shortest to longest. The diagram is not to scale. 31. Two sides of a triangle have lengths 10 and 17. What must be true about the length of the third side? 8

32. What is the range of possible values for x? The diagram is not to scale. 33. What is the range of possible values for x? The diagram is not to scale. 9

34. What is the range of possible values for x? 35. What are the missing reasons in the two-column proof? Given: JM ML and m JMK m KML Prove: JK KL Statements Reasons 1. JM ML 1. Given 2. KM KM 2.? 3. m JMK m KML 3. Given 4. JK KL 4.? 10

Geometry M1: Unit 3 Practice Exam Answer Section SHORT ANSWER 1. ANS: 66 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Converse of Isosceles Triangle Theorem Triangle Angle-Sum Theorem 2. ANS: 84 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Isosceles Triangle Theorem Triangle Angle-Sum Theorem word problem 3. ANS: 34.5 PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 2 Using Algebra KEY: Isosceles Triangle Theorem Triangle Angle-Sum Theorem isosceles triangle 4. ANS: 19 PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 2 Using Algebra KEY: Isosceles Triangle Theorem isosceles triangle problem solving Triangle Angle-Sum Theorem 5. ANS: 10 x only PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 2 Using Algebra KEY: equilateral triangle word problem problem solving DOK: DOK 3 1

6. ANS: 1 PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Isosceles Triangle Theorem word problem problem solving DOK: DOK 3 7. ANS: x 90, y 30 PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 2 Using Algebra KEY: angle bisector isosceles triangle 8. ANS: 73 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 3 Finding Angle Measures KEY: Isosceles Triangle Theorem isosceles triangle Triangle Angle-Sum Theorem word problem problem solving 9. ANS: x 22 PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Problem 3 Finding Angle Measures KEY: Isosceles Triangle Theorem isosceles triangle 10. ANS: 40 PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1 MA.912.G.4.5 TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint midsegment Triangle Midsegment Theorem 11. ANS: 7 PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1 MA.912.G.4.5 TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint midsegment Triangle Midsegment Theorem 2

12. ANS: 88 PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1 MA.912.G.4.5 TOP: 5-1 Problem 2 Finding Lengths KEY: midsegment Triangle Midsegment Theorem 13. ANS: 12.5 PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1 MA.912.G.4.5 TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint midsegment Triangle Midsegment Theorem 14. ANS: 23 PTS: 1 DIF: L4 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1 MA.912.G.4.5 TOP: 5-1 Problem 2 Finding Lengths KEY: midsegment Triangle Midsegment Theorem 15. ANS: 65 ft PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1 MA.912.G.4.5 TOP: 5-1 Problem 3 Using a Midsegment of a Triangle KEY: midsegment Triangle Midsegment Theorem problem solving DOK: DOK 1 16. ANS: 38º PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1 MA.912.G.4.5 TOP: 5-1 Problem 3 Using a Midsegment of a Triangle KEY: midsegment Triangle Midsegment Theorem problem solving DOK: DOK 1 17. ANS: 6 PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectors STA: MA.912.G.4.2 TOP: 5-2 Problem 3 Using the Angle Bisector Theorem KEY: Angle Bisector Theorem angle bisector 3

18. ANS: 54 PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectors STA: MA.912.G.4.2 TOP: 5-2 Problem 3 Using the Angle Bisector Theorem KEY: Converse of the Angle Bisector Theorem angle bisector 19. ANS: 12 PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectors STA: MA.912.G.4.2 TOP: 5-2 Problem 3 Using the Angle Bisector Theorem KEY: angle bisector Angle Bisector Theorem 20. ANS: 6 PTS: 1 DIF: L2 REF: 5-2 Perpendicular and Angle Bisectors OBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectors STA: MA.912.G.4.2 TOP: 5-2 Problem 3 Using the Angle Bisector Theorem KEY: angle bisector Converse of the Angle Bisector Theorem 21. ANS: ( 1 2, 1 2 ) PTS: 1 DIF: L3 REF: 5-3 Bisectors in Triangles OBJ: 5-3.1 Identify properties of perpendicular bisectors and angle bisectors STA: MA.912.G.1.1 MA.912.G.4.2 MA.912.G.6.1 TOP: 5-3 Problem 1 Finding the Circumcenter of a Triangle KEY: circumscribe circumcenter of the triangle 22. ANS: (5, 2) PTS: 1 DIF: L3 REF: 5-3 Bisectors in Triangles OBJ: 5-3.1 Identify properties of perpendicular bisectors and angle bisectors STA: MA.912.G.1.1 MA.912.G.4.2 MA.912.G.6.1 TOP: 5-3 Problem 1 Finding the Circumcenter of a Triangle KEY: circumcenter of the triangle circumscribe 23. ANS: 11 PTS: 1 DIF: L2 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 Identify properties of medians and altitudes of a triangle STA: MA.912.G.4.2 MA.912.G.4.5 TOP: 5-4 Problem 1 Finding the Length of a Median KEY: median of a triangle DOK: DOK 1 4

24. ANS: BG 7, GE 14 PTS: 1 DIF: L3 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 Identify properties of medians and altitudes of a triangle STA: MA.912.G.4.2 MA.912.G.4.5 TOP: 5-4 Problem 1 Finding the Length of a Median KEY: centroid median of a triangle DOK: DOK 1 25. ANS: 14 PTS: 1 DIF: L4 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 Identify properties of medians and altitudes of a triangle STA: MA.912.G.4.2 MA.912.G.4.5 TOP: 5-4 Problem 1 Finding the Length of a Median KEY: centroid median of a triangle 26. ANS: QS PTS: 1 DIF: L3 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 Identify properties of medians and altitudes of a triangle STA: MA.912.G.4.2 MA.912.G.4.5 TOP: 5-4 Problem 2 Identifying Medians and Altitudes KEY: median of a triangle DOK: DOK 1 27. ANS: altitude PTS: 1 DIF: L2 REF: 5-4 Medians and Altitudes OBJ: 5-4.1 Identify properties of medians and altitudes of a triangle STA: MA.912.G.4.2 MA.912.G.4.5 TOP: 5-4 Problem 2 Identifying Medians and Altitudes KEY: altitude of a triangle angle bisector perpendicular bisector midsegment median of a triangle DOK: DOK 1 28. ANS: 2 PTS: 1 DIF: L4 REF: 5-6 Inequalities in One Triangle OBJ: 5-6.1 Use inequalities involving angles and sides of triangles STA: MA.912.G.4.7 TOP: 5-6 Problem 2 Using Theorem 5-10 KEY: corollary to the Triangle Exterior Angle Theorem 29. ANS: AB; AC; BC PTS: 1 DIF: L4 REF: 5-6 Inequalities in One Triangle OBJ: 5-6.1 Use inequalities involving angles and sides of triangles STA: MA.912.G.4.7 TOP: 5-6 Problem 3 Using Theorem 5-11 KEY: multi-part question 5

30. ANS: LK, LJ, JK PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle OBJ: 5-6.1 Use inequalities involving angles and sides of triangles STA: MA.912.G.4.7 TOP: 5-6 Problem 3 Using Theorem 5-11 DOK: DOK 1 31. ANS: less than 27 PTS: 1 DIF: L3 REF: 5-6 Inequalities in One Triangle OBJ: 5-6.1 Use inequalities involving angles and sides of triangles STA: MA.912.G.4.7 TOP: 5-6 Problem 5 Finding Possible Side Lengths KEY: Triangle Inequality Theorem 32. ANS: 0 x 33 PTS: 1 DIF: L2 REF: 5-7 Inequalities in Two Triangles OBJ: 5-7.1 Apply inequalities in two triangles STA: MA.912.G.4.7 TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem 33. ANS: 11 x 43 PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two Triangles OBJ: 5-7.1 Apply inequalities in two triangles STA: MA.912.G.4.7 TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem 34. ANS: 4 x 18 PTS: 1 DIF: L4 REF: 5-7 Inequalities in Two Triangles OBJ: 5-7.1 Apply inequalities in two triangles STA: MA.912.G.4.7 TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem 35. ANS: 2. Reflexive Property 4. Hinge Theorem PTS: 1 DIF: L2 REF: 5-7 Inequalities in Two Triangles OBJ: 5-7.1 Apply inequalities in two triangles STA: MA.912.G.4.7 TOP: 5-7 Problem 4 Proving Relationships in Triangles 6

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