Geo - CH6 Practice Test

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1 Geo - H6 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measure of each exterior angle of a regular decagon. a. 45 c. 18 b d The diagram shows the parallelogram-shaped component that attaches a car s rearview mirror to the car. In parallelogram RSTU, UR = 25, RX = 16, and m STU = 42.4 o. Find ST, XT, and m RST. a. ST = 16, m RST = 42.4, XT = 25 c. ST = 25, m RST = 137.6, XT = 16 b. ST = 25, m RST = 47.8, XT = 16 d. ST = 5, m RST = 137.6, XT = 4 3. MNOP is a parallelogram. Find MP. a. MP = 25 c. MP = 20 b. MP = 30 d. MP = 6 4. Write a two-column proof. Given: F and F are parallelograms. Prove: F omplete the proof.

2 Proof: Statements Reasons 1. F and F are parallelograms. 1. Given 2. F 2. [1] 3. F Ä 3. Opposite sides in a parallelogram are parallel. 4. F F 4. [2] 5. F 5. Substitution a. [1] In a parallelogram, opposite angles are congruent. [2] lternate Interior ngles Theorem b. [1] Vertical ngles Theorem [2] lternate Exterior ngles Theorem c. [1] PT [2] In a parallelogram, opposite angles are congruent. d. [1] In a parallelogram, consecutive angles are congruent. [2] In a parallelogram, all angles are congruent. 5. Show that GHIJ is a parallelogram for x = 5 and y = 8. omplete the explanation. HI = 5x 10 GJ = 7x 20 Given HI = 5(5) 10 = [1] GJ = 7(5) 20 = [2] Substitute and simplify. GH = 3y JI = 5y 16 Given GH = 3(8) = [3] JI = 5(8) 16 = [4] Substitute and simplify. Since HI = GJ and GH = JI, GHIJ is a parallelogram because [5]. a. [1] 15 [2] 15 [3] 24 [4] 24 [5] both sets of opposite sides are congruent. b. [1] 15 [2] 24 [3] 15 [4] 24 [5] one set of opposite sides is parallel and congruent. c. [1] 15

3 [2] 15 [3] 24 [4] 24 [5] both sets of opposite sides are parallel. d. [1] 24 [2] 24 [3] 15 [4] 15 [5] both sets of opposite angles are congruent. 6. Show that quadrilateral EFG is a parallelogram. slope of E = ( 5) = 3 8 slope of FG = = 3 8 E = (3 ( 5)) 2 + (10 7) 2 = 73 FG = (8 0) 2 + (4 1) 2 = 73 omplete the explanation. E and FG have the same slope, so [1]. Since E = FG, [2]. ecause [3], EFG is a parallelogram. a. [1] E FG [2] E FG [3] One pair of opposite sides is equal and perpendicular. b. [1] E Ä FG [2] E FG [3] One pair of opposite sides is parallel and congruent. c. [1] E Ä FG [2] E ~ FG [3] One pair of opposite sides is parallel and in proportion. d. [1] E FG [2] E FG [3] One pair of opposite sides is not congruent but is perpendicular. 7. n artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center of the quilt. The dimensions of the rectangle are = 10 inches and = 14 inches. Find X.

4 a. X = 7 inches c. X = 5 inches b. X = 10 inches d. X = 14 inches 8. Show that all four sides of square are congruent and that. a. = 3 5, = 3 5, = 3 5, = 3 5, slope of = 2, slope of = 1 2. Since the product of the slopes is 1,. b. = 9 2, = 9 2, = 9 2, = 9 2, slope of = 2, slope of = 1 2. Since the product of the slopes is 1,. c. = 3 5, = 3 5, = 3 5, = 3 5, slope of = 1 2, slope of = 2. Since the product of the slopes is 1,. d. = 4, = 4, = 4, = 4, slope of = 2, slope of = 1 2. Since the product of the slopes is 1,. 9. The side of a wooden chest is a quadrilateral with Ä, and Ä. If m = 90, what is the most accurate description of?

5 a. oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a rectangle. b. oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a square. c. oth pairs of opposite sides are parallel so is a rhombus. Since one angle measures 90, it is a right angle and a rhombus with one right angle is a square. d. oth pairs of opposite sides are parallel so is a parallelogram. One angle measuring 90 does not provide enough information to change its description. 10. etermine if the conclusion is valid. If not, tell what additional information is needed to make it valid. Given:,, and onclusion: is a square. a. Opposite sides are congruent, so is a parallelogram. iagonals are congruent, so is a rectangle. Two consecutive sides are not congruent, so is not a square. b. Opposite sides are congruent, so is a rhombus. iagonals are congruent, so is a rectangle. quadrilateral that is a rhombus and a rectangle is a square, so is a square. c. Opposite sides are congruent, so is a parallelogram. iagonals are congruent, so is a rhombus. One angle is not a right angle, so is not a square. d. Opposite sides are congruent, so is a rhombus. iagonals are congruent, so is a square.

6 11. Use the diagonals to determine whether a parallelogram with vertices ( 1, 2), ( 2, 0), (0, 1), and (1, 1)is a rectangle, rhombus, or square. Give all the names that apply. a. rectangle, rhombus, square c. rectangle b. rectangle, rhombus d. square Numeric Response 12. In parallelogram LMNO, NO = 10.2, and LO = What is the perimeter of parallelogram LMNO? 13. Find the value of x in the rhombus. Matching Match each vocabulary term with its definition. a. concave b. convex c. diagonal d. regular polygon e. side of a polygon f. vertex of a polygon g. quadrilateral h. trapezoid 14. a segment that connects any two nonconsecutive vertices of a polygon 15. a polygon in which no diagonal contains points in the exterior of the polygon 16. one of the segments that forms a polygon 17. a polygon that is both equilateral and equiangular 18. the common endpoint of two sides of the polygon Match each vocabulary term with its definition. a. kite b. trapezoid c. rectangle

7 d. polygon e. square f. rhombus g. parallelogram 19. a quadrilateral with four right angles 20. a quadrilateral with four congruent sides and four right angles 21. a quadrilateral with four congruent sides 22. a quadrilateral with two pairs of parallel sides 23. a quadrilateral with exactly two pairs of congruent consecutive sides

8 Geo - H6 Practice Test nswer Section MULTIPLE HOIE 1. NS: decagon has 10 sides and 10 vertices. sum of exterior angle measures = 360 measure of one exterior angle = = 36 Polygon Exterior ngle Sum Theorem regular decagon has 10 congruent exterior angles, so divide the sum by 10. The measure of each exterior angle of a regular decagon is 36. ivide by the number of sides the polygon has. ivide 360 by the number of sides the polygon has. ivide 360 by the number of sides. orrect! PTS: 1 IF: verage REF: Page 384 OJ: Finding Exterior ngle Measures in Polygons NT: f TOP: 6-1 Properties and ttributes of Polygons 2. NS: To find ST: ST UR In a parallelogram, opposite sides are congruent. ST = UR efinition of congruent segments ST = 25 Substitute 25 for UR. To find XT: XT RX XT = RX XT = 16 In a parallelogram, diagonals bisect each other. efinition of congruent segments Substitute 16 for RX. To find m RST: m RST + m STU = 180 In a parallelogram, consecutive angles are supplementary. m RST = 180 Substitute 42.4 for m STU. m RST = Subtract 42.4 from both sides. In a parallelogram, consecutive angles are supplementary, opposite sides are congruent, and diagonals bisect each other. In a parallelogram, consecutive angles are supplementary not complementary. orrect!

9 Opposite sides of a parallelogram are congruent, and diagonals bisect each other. PTS: 1 IF: verage REF: Page 392 OJ: pplication NT: f TOP: 6-2 Properties of Parallelograms 3. NS: MP NO Opposite sides of a parallelogram are congruent. MP = NO efinition of congruent segments 5x = 3x + 12 Substitute. x = 6 Simplify and solve. MP = 5x = 5(6) = 30 Substitute and solve for entire segment measure. Opposite sides of a parallelogram are congruent. orrect! Set the expressions for opposite sides of the parallelogram equal to each other. Substitute the solution for x back into the original expression. PTS: 1 IF: verage REF: Page 393 OJ: Using Properties of Parallelograms to Find Measures NT: f TOP: 6-2 Properties of Parallelograms 4. NS: Proof: Statements Reasons 1. F and F are parallelograms. 1. Given 2. F 2. In a parallelogram, opposite angles are congruent. 3. F Ä 3. Opposite sides in a parallelogram are parallel. 4. F F 4. lternate Interior ngles Theorem 5. F 5. Substitution orrect! ngle and angle F are not vertical angles. Triangles have not been proven congruent. In a parallelogram, only opposite angles must be congruent. PTS: 1 IF: verage REF: Page 394 OJ: Using Properties of Parallelograms in a Proof NT: a TOP: 6-2 Properties of Parallelograms 5. NS: HI = 5x 10 GJ = 7x 20 Given HI = 5(5) 10 = 15 GJ = 7(5) 20 = 15 Substitute and simplify.

10 GH = 3y JI = 5y 16 Given GH = 3(8) = 24 JI = 5(8) 16 = 24 Substitute and simplify. Since HI = GJ and GH = JI, GHIJ is a parallelogram because both sets of opposite sides are congruent. orrect! Information about both sets of opposite sides of the quadrilateral was calculated. To make a conclusion about sides being parallel, slope would need to be calculated. e careful about determining which number goes in which blank! PTS: 1 IF: verage REF: Page 399 OJ: Verifying Figures are Parallelograms TOP: 6-3 onditions for Parallelograms 6. NS: Find the slopes and lengths of one pair of opposite sides. slope of E = ( 5) = 3 8 slope of FG = = 3 8 E = (3 ( 5)) 2 + (10 7) 2 = 73 NT: f FG = (8 0) 2 + (4 1) 2 = 73 E and FG have the same slope, so E Ä FG. Since E = FG, E FG. ecause one pair of opposite sides is both congruent and parallel, EFG is a parallelogram. When slopes are the same, lines are parallel. orrect! If sides are equal in length, then they are congruent. Perpendicular lines do not have the same slope. PTS: 1 IF: verage REF: Page 400 OJ: Proving Parallelograms in the oordinate Plane NT: g TOP: 6-3 onditions for Parallelograms 7. NS: = = 14 The diagonals of a rectangle are congruent. X = 1 rectangle is a parallelogram. The diagonals of a parallelogram 2 bisect each other. Substitute and simplify. X = 1 2 (14) = 7

11 orrect! The diagonals of a rectangle are congruent. The diagonals of a rectangle are congruent. The diagonals of a rectangle bisect each other. PTS: 1 IF: asic REF: Page 408 OJ: pplication NT: f TOP: 6-4 Properties of Special Parallelograms 8. NS: = ( 1 ( 4)) 2 + (3 ( 3)) 2 = 3 5 = (5 ( 1)) 2 + (0 3) 2 = 3 5 = (2 5) 2 + ( 6 0) 2 = 3 5 = ( 4 2) 2 + ( 3 ( 6)) 2 = 3 5 slope of = 3 ( 3) 1 ( 4) = 2 slope of = ( 1) = Ê Ë Á 1 2 ˆ = 1 Since the product of the slopes is 1,. orrect! Use the distance formula to find the measures of the lengths of the sides of the square. The slope of a line is the difference in y-coordinates divided by the difference in the x-coordinates. Use the distance formula to find the measures of the lengths of the sides of the square. PTS: 1 IF: verage REF: Page 410 OJ: Verifying Properties of Squares NT: a TOP: 6-4 Properties of Special Parallelograms 9. NS: oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a rectangle. orrect! square is a parallelogram with one right angle N two consecutive congruent sides. Find the shape with one right angle, but not necessarily two consecutive congruent sides. rhombus has parallel opposite sides, but it also has other restrictions. Find the

12 shape without the other restrictions. parallelogram with one right angle OES provide enough information to change its description. PTS: 1 IF: verage REF: Page 418 OJ: pplication NT: f TOP: 6-5 onditions for Special Parallelograms 10. NS: Opposite sides are congruent, so is a parallelogram. iagonals are congruent, so is a rectangle. Two consecutive sides are not congruent, so is not a square. orrect! If opposite sides are congruent, the quadrilateral is not necessarily a rhombus. Find a description with fewer restrictions. If diagonals of a parallelogram are congruent, a different shape is created. If opposite sides are congruent, the quadrilateral is not necessarily a rhombus. Find a description with fewer restrictions. PTS: 1 IF: verage REF: Page 420 OJ: pplying onditions for Special Parallelograms TOP: 6-5 onditions for Special Parallelograms 11. NS: Step 1 Graph. NT: f Step 2 The diagonals of a rectangle are congruent. Find and to determine if is a rectangle. = (0 ( 1_ ) 2 + (1 ( 2)) 2 = 10 = (1 ( 2)) 2 + ( 1 0) 2 = 10 Since =, is a rectangle. Step 3 The diagonals of a rhombus are perpendicular. Find the slopes of and to determine if is a rhombus.

13 slope of = 1 ( 2) 0 ( 1) = 3 slope of = ( 2) = 1 3 Since (3) ÊÁ Ë 1 3 ˆ = 1, and is a rhombus. Since is both a rhombus and a rectangle, it is also a square. orrect! quadrilateral that is a rectangle and a rhombus is also something else. Find the slopes of the diagonals of to determine if the shape is a rhombus. etermine if the quadrilateral is a rectangle by finding the measures of its diagonals. PTS: 1 IF: verage REF: Page 420 OJ: Identifying Special Parallelograms in the oordinate Plane NT: d TOP: 6-5 onditions for Special Parallelograms NUMERI RESPONSE 12. NS: 49.8 PTS: 1 IF: verage NT: h TOP: 6-2 Properties of Parallelograms 13. NS: 0.5 PTS: 1 IF: dvanced NT: f TOP: 6-4 Properties of Special Parallelograms MTHING 14. NS: PTS: 1 IF: asic REF: Page 382 TOP: 6-1 Properties and ttributes of Polygons 15. NS: PTS: 1 IF: asic REF: Page 383 TOP: 6-1 Properties and ttributes of Polygons 16. NS: E PTS: 1 IF: asic REF: Page 382 TOP: 6-1 Properties and ttributes of Polygons 17. NS: PTS: 1 IF: asic REF: Page 382 TOP: 6-1 Properties and ttributes of Polygons 18. NS: F PTS: 1 IF: asic REF: Page 382 TOP: 6-1 Properties and ttributes of Polygons 19. NS: PTS: 1 IF: asic REF: Page 408

14 TOP: 6-4 Properties of Special Parallelograms 20. NS: E PTS: 1 IF: asic REF: Page 410 TOP: 6-4 Properties of Special Parallelograms 21. NS: F PTS: 1 IF: asic REF: Page 409 TOP: 6-4 Properties of Special Parallelograms 22. NS: G PTS: 1 IF: asic REF: Page 391 TOP: 6-2 Properties of Parallelograms 23. NS: PTS: 1 IF: asic REF: Page 427 TOP: 6-6 Properties of Kites and Trapezoids

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