Name: ________________________ Class: ___________________ Date: __________ ID: A

1

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?

Name: ________________________ ID: A

2

4. Find the value of x. The diagram is not to scale.

Given: RS ST , mRST 5x 47, mSTU 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.

Name: ________________________ ID: A

3

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.

Name: ________________________ ID: A

4

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.

Name: ________________________ ID: A

5

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 mRST. The diagram is not to scale.

Name: ________________________ ID: A

6

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).

Name: ________________________ ID: A

7

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.

Name: ________________________ ID: A

8

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. mA 9x 7, mB 7x 9, and mC 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?

Name: ________________________ ID: A

9

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.

Name: ________________________ ID: A

10

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 mJMK mKMLProve: JK KL

Statements Reasons1. JM ML 1. Given2. KM KM 2. ? 3. mJMK mKML 3. Given4. JK KL 4. ?

ID: A

1

Geometry M1: Unit 3 Practice ExamAnswer Section

SHORT ANSWER

1. ANS: 66°

PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using AlgebraKEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum TheoremDOK: DOK 2

2. ANS: 84°

PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using AlgebraKEY: isosceles triangle | Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | word problemDOK: DOK 2

3. ANS: 34.5°

PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using AlgebraKEY: Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | isosceles triangleDOK: DOK 2

4. ANS: 19

PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using AlgebraKEY: Isosceles Triangle Theorem | isosceles triangle | problem solving | Triangle Angle-Sum TheoremDOK: DOK 2

5. ANS: 10 – x only

PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using AlgebraKEY: equilateral triangle | word problem | problem solving DOK: DOK 3

ID: A

2

6. ANS: 1

PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using AlgebraKEY: isosceles triangle | Isosceles Triangle Theorem | word problem | problem solvingDOK: DOK 3

7. ANS: x 90, y 30

PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 2 Using AlgebraKEY: angle bisector | isosceles triangle DOK: DOK 2

8. ANS: 73

PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 3 Finding Angle MeasuresKEY: Isosceles Triangle Theorem | isosceles triangle | Triangle Angle-Sum Theorem | word problem | problem solving DOK: DOK 2

9. ANS: x 22

PTS: 1 DIF: L4 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 Use and apply properties of isosceles and equilateral trianglesSTA: MA.912.G.4.1 TOP: 4-5 Problem 3 Finding Angle MeasuresKEY: Isosceles Triangle Theorem | isosceles triangle DOK: DOK 2

10. ANS: 40

PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1| MA.912.G.4.5TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint | midsegment | Triangle Midsegment TheoremDOK: DOK 2

11. ANS: 7

PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1| MA.912.G.4.5TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint | midsegment | Triangle Midsegment TheoremDOK: DOK 2

ID: A

3

12. ANS: 88

PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1| MA.912.G.4.5TOP: 5-1 Problem 2 Finding Lengths KEY: midsegment | Triangle Midsegment TheoremDOK: DOK 2

13. ANS: 12.5

PTS: 1 DIF: L2 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1| MA.912.G.4.5TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint | midsegment | Triangle Midsegment TheoremDOK: DOK 2

14. ANS: 23

PTS: 1 DIF: L4 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1| MA.912.G.4.5TOP: 5-1 Problem 2 Finding Lengths KEY: midsegment | Triangle Midsegment TheoremDOK: DOK 2

15. ANS: 65 ft

PTS: 1 DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1| MA.912.G.4.5TOP: 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 TrianglesOBJ: 5-1.1 Use properties of midsegments to solve problems STA: MA.912.G.1.1| MA.912.G.4.5TOP: 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 BisectorsOBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectorsSTA: MA.912.G.4.2 TOP: 5-2 Problem 3 Using the Angle Bisector TheoremKEY: Angle Bisector Theorem | angle bisector DOK: DOK 2

ID: A

4

18. ANS: 54

PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle BisectorsOBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectorsSTA: MA.912.G.4.2 TOP: 5-2 Problem 3 Using the Angle Bisector TheoremKEY: Converse of the Angle Bisector Theorem | angle bisector DOK: DOK 2

19. ANS: 12

PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle BisectorsOBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectorsSTA: MA.912.G.4.2 TOP: 5-2 Problem 3 Using the Angle Bisector TheoremKEY: angle bisector | Angle Bisector Theorem DOK: DOK 2

20. ANS: 6

PTS: 1 DIF: L2 REF: 5-2 Perpendicular and Angle BisectorsOBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectorsSTA: MA.912.G.4.2 TOP: 5-2 Problem 3 Using the Angle Bisector TheoremKEY: angle bisector | Converse of the Angle Bisector Theorem DOK: DOK 2

21. ANS:

(12

, 12

)

PTS: 1 DIF: L3 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 Identify properties of perpendicular bisectors and angle bisectorsSTA: 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 DOK: DOK 2

22. ANS: (5, 2)

PTS: 1 DIF: L3 REF: 5-3 Bisectors in TrianglesOBJ: 5-3.1 Identify properties of perpendicular bisectors and angle bisectorsSTA: 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 DOK: DOK 2

23. ANS: 11

PTS: 1 DIF: L2 REF: 5-4 Medians and AltitudesOBJ: 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 MedianKEY: median of a triangle DOK: DOK 1

ID: A

5

24. ANS: BG 7, GE 14

PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 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 MedianKEY: centroid | median of a triangle DOK: DOK 1

25. ANS: 14

PTS: 1 DIF: L4 REF: 5-4 Medians and AltitudesOBJ: 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 MedianKEY: centroid | median of a triangle DOK: DOK 2

26. ANS:

QS

PTS: 1 DIF: L3 REF: 5-4 Medians and AltitudesOBJ: 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 AltitudesKEY: median of a triangle DOK: DOK 1

27. ANS: altitude

PTS: 1 DIF: L2 REF: 5-4 Medians and AltitudesOBJ: 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 AltitudesKEY: altitude of a triangle | angle bisector | perpendicular bisector | midsegment | median of a triangleDOK: DOK 1

28. ANS: 2

PTS: 1 DIF: L4 REF: 5-6 Inequalities in One TriangleOBJ: 5-6.1 Use inequalities involving angles and sides of triangles STA: MA.912.G.4.7 TOP: 5-6 Problem 2 Using Theorem 5-10KEY: corollary to the Triangle Exterior Angle Theorem DOK: DOK 2

29. ANS:

AB; AC; BC

PTS: 1 DIF: L4 REF: 5-6 Inequalities in One TriangleOBJ: 5-6.1 Use inequalities involving angles and sides of triangles STA: MA.912.G.4.7 TOP: 5-6 Problem 3 Using Theorem 5-11KEY: multi-part question DOK: DOK 2

ID: A

6

30. ANS:

LK , LJ , JK

PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 5-6.1 Use inequalities involving angles and sides of triangles STA: MA.912.G.4.7 TOP: 5-6 Problem 3 Using Theorem 5-11DOK: DOK 1

31. ANS: less than 27

PTS: 1 DIF: L3 REF: 5-6 Inequalities in One TriangleOBJ: 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 LengthsKEY: Triangle Inequality Theorem DOK: DOK 2

32. ANS: 0 x 33

PTS: 1 DIF: L2 REF: 5-7 Inequalities in Two TrianglesOBJ: 5-7.1 Apply inequalities in two triangles STA: MA.912.G.4.7TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem DOK: DOK 2

33. ANS: 11 x 43

PTS: 1 DIF: L3 REF: 5-7 Inequalities in Two TrianglesOBJ: 5-7.1 Apply inequalities in two triangles STA: MA.912.G.4.7TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem DOK: DOK 2

34. ANS: 4 x 18

PTS: 1 DIF: L4 REF: 5-7 Inequalities in Two TrianglesOBJ: 5-7.1 Apply inequalities in two triangles STA: MA.912.G.4.7TOP: 5-7 Problem 3 Using the Converse of the Hinge Theorem DOK: DOK 2

35. ANS: 2. Reflexive Property4. Hinge Theorem

PTS: 1 DIF: L2 REF: 5-7 Inequalities in Two TrianglesOBJ: 5-7.1 Apply inequalities in two triangles STA: MA.912.G.4.7TOP: 5-7 Problem 4 Proving Relationships in Triangles DOK: DOK 2