Practice Problems for Chapter 1 Exam Chapter 1 Review Practice Problems for Chapter 1 Exam

1. What is the intersection of plane XWST and plane ZWSV? 𝑆𝑊 𝑉𝑍 𝑆𝑇 𝑇𝑋 Non-Response Grid

𝑆𝑊 Answer is A because two planes intersect in a line and plane XWST and plane ZWSV have point S and point W in common.

2. Name an angle complementary to ∠𝐵𝑂𝐶. ∠𝐴𝑂𝐵 ∠𝐷𝑂𝐶 ∠𝐸𝑂𝐵 ∠𝐸𝑂𝐷 Non-Response Grid

∠𝐷𝑂𝐶 The answer is B because angle AOB is right which makes angle BOD right and m ∠𝐵𝑂𝐶 + m ∠𝐷𝑂𝐶 = 90 degrees.

3. Match the isometric drawing with the correct orthographic drawing. Non-Response Grid

The answer is C because it shows the correct top right and front sides.

4. Find the area of the circle to the nearest tenth. Use 3.14 for  . Non-Response Grid

The answer is A. Diameter is 12.2 in so the radius is 6.1 in. Area is 𝜋 𝑟 2 so 𝜋 (6.1) 2 =37.21𝜋 = 37.21(3.14) = 116.8394 = 116.8 in2

5. 𝑀𝑂 bisects ∠LMN, m∠LMO =8x 25, and m∠NMO =2x + 41 5. 𝑀𝑂 bisects ∠LMN, m∠LMO =8x 25, and m∠NMO =2x + 41. Solve for x and find m∠LMN. The diagram is not to scale. x = 11, m∠LMN=126 x = 11, m∠LMN=63 x = 10, m∠LMN=110 x = 10, m∠LMN=55 Non-Response Grid

The answer is A.x = 11, m∠LMN=126 Bisects means the angles are equal so set them equal to each other and solve. 8x 25 = 2x + 41 6𝑥=41+25=66 𝑥=11 8 11 −25=63 2 11 +41=63 So the whole angle measures 126 degrees

6. Name an angle vertical to ∠𝐻𝐺𝐽. ∠𝐽𝐺𝐹 ∠𝐻𝐺𝐸 ∠𝐹𝐺𝐼 ∠𝐹𝐺𝐷 Non-Response Grid

Vertical angles make an x so across from ∠HGJ is ∠FGD Vertical angles make an x so across from ∠HGJ is ∠FGD. The correct answer is D.

7. What is the name of the ray that is opposite 𝐶𝐷 ? 𝐴𝐷 𝐵𝐷 𝐶𝐴 Non-Response Grid

The name of the ray that is opposite 𝐶𝐷 is either 𝐶𝐵 or 𝐶𝐴. So the correct answer is D.

8. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 2) and K(4, 10). (6, 12) (2, 8) (1, 4) (3, 6) Non-Response Grid

The answer is D. Average the x coordinates and the y coordinates. 2+4 2 , 2+10 2 = 3, 6

9. Nate wants to put a fence around his rectangular garden 9. Nate wants to put a fence around his rectangular garden. His garden measures 39 feet by 48 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Nate need to enclose the garden and path? 99 𝑓𝑒𝑒𝑡 198 𝑓𝑒𝑒𝑡 150 𝑓𝑒𝑒𝑡 186 𝑓𝑒𝑒𝑡 Non-Response Grid

The answer is B. 48 ft 39 ft 3 ft Since the pathway is on both sides you must add 6 to each dimension to find the new perimeter. 48 + 6 = 54 and 39 + 6 = 45. P = 2(54) + 2(45) =198 FEET OF FENCE NEEDED.

10. Complete the statement. ∠𝐺𝐹𝐷 ≅∠ ______. ∠𝐷𝐹𝐸 ∠𝐸𝐷𝐹 ∠𝐷𝐺𝐹 ∠𝐷𝐸𝐹 Non-Response Grid

The answer is A. The angle congruent to ∠𝐺𝐹𝐷 is ∠𝐷𝐹𝐸. They have the same markings.

11. If Z is the midpoint of 𝑅𝑇 what are x, RZ, and RT? Non-Response Grid

The correct answer is A. x = 4, RZ = 9, and RT = 18 Midpoint means middle so RZ = ZT. 8𝑥 −23=9 8𝑥=9+23=32 8𝑥=32 𝑥=4 𝑅𝑍=8 4 −23=32 −23=9 𝑅𝑍+𝑅𝑇=9+9=18

m∠𝐴𝐵𝐸= 90 o ;∠𝐴𝐵𝐸 is right. m∠DBC= 164 𝑜 ;∠DBC is obtuse. 12. What are the measures of ∠𝐴𝐵𝐸 and ∠DBC? Classify each angle as acute, right, obtuse, or straight. m∠𝐴𝐵𝐸= 90 o ;∠𝐴𝐵𝐸 is right. m∠DBC= 164 𝑜 ;∠DBC is obtuse. m∠𝐴𝐵𝐸= 80 o ;∠𝐴𝐵𝐸 is obtuse. m∠DBC= 164 𝑜 ;∠DBC is acute. m∠𝐴𝐵𝐸= 80 o ;∠𝐴𝐵𝐸 is acute. m∠DBC= 154 𝑜 ;∠DBC is obtuse. m∠𝐴𝐵𝐸= 80 o ;∠𝐴𝐵𝐸 is acute. m∠DBC= 164 𝑜 ;∠DBC is obtuse. Non-Response Grid

The answer is D. m∠𝐴𝐵𝐸= 80 o ;∠𝐴𝐵𝐸 is acute The answer is D. m∠𝐴𝐵𝐸= 80 o ;∠𝐴𝐵𝐸 is acute. m∠DBC= 164 𝑜 ;∠DBC is obtuse. Since m∠𝐴𝐵𝐸= 80 o ;∠𝐴𝐵𝐸 is acute. And since m∠DBC =164 𝑜 ∠DBC is obtuse.

13. T(6, 11) is the midpoint of 𝐶𝐷. The coordinates of D are (6, 17) 13. T(6, 11) is the midpoint of 𝐶𝐷 . The coordinates of D are (6, 17). What are the coordinates of C? (6, 22) (6, 5) (6, 14) (6, 23) Non-Response Grid

The correct answer is B. (6, 5) T(6, 11) is the midpoint of 𝐶𝐷 . The coordinates of D are (6, 17). What are the coordinates of C? 6, 11 = 6+𝑥 2 , 17+𝑦 2 6= 6+𝑥 2 11= 17+𝑦 2 12=6+𝑥 22=17+𝑦 6=𝑥 5=𝑦 6, 5

14. Find the distance between points P(7, 3) and Q(2, 5) to the nearest tenth. 5.4 7 29 12 Non-Response Grid

The answer is A. 5.4 2 −7 2 + 3−5 2 −5 2 + −2 2 25+4 29 ≈5.4

15. What are the names of three collinear points? Points D, J, and B are collinear. Points A, J, and B are collinear. Points D, J, and K are collinear. Points L, J, and K are collinear. Non-Response Grid

The answer is D. Points L, J, and K are collinear. Collinear means they are on the same line.

16. When the net is folded into the rectangular prism shown beside it, which letters will be on the front and bottom of the rectangular prism? The letter on the front will be W. The letter on the bottom will be U. The letter on the front will be X. The letter on the bottom will be U. The letter on the front will be W. The letter on the bottom will be X. The letter on the front will be X. The letter on the bottom will be W. Non-Response Grid

The answer is C. The letter on the front will be W The answer is C.The letter on the front will be W. The letter on the bottom will be X. W will be on the front when you fold V over to make the top and that makes X the bottom of the box.

17. Find the circumference of the circle to the nearest tenth. Use 3 17. Find the circumference of the circle to the nearest tenth. Use 3.14 for . 163.3 m 530.7 m 81.6 m 40.8 m Non-Response Grid

The answer is C. 81.6 m Circumference is 𝑑. 𝜋 2𝑟 = 𝜋 26 3.14 26 =81.64 𝑚 2

18. Find the area of a rectangle with base of 66 cm and a height of 5 m. Non-Response Grid

The answer is C. 33,000 cm2 Find the area of a rectangle with base of 66 cm and a height of 5 m. First covert 5 m to 500 cm. Area is 𝑏ℎ. So 66 500 =33,000 𝑐𝑚 2

𝑚∠𝐵𝑂𝐶= 38 𝑜 , 𝑚∠𝐴𝑂𝐵= 41 𝑜 𝑚∠𝐵𝑂𝐶= 41 𝑜 , 𝑚∠𝐴𝑂𝐵= 38 𝑜 19. If 𝑚∠𝐴𝑂𝐶= 79 𝑜 , 𝑚∠𝐵𝑂𝐶=2𝑥+10, and 𝑚∠𝐴𝑂𝐵=4𝑥−15, find the degree measure of∠𝐵𝑂𝐶 and ∠𝐴𝑂𝐵. The diagram is not to scale. 𝑚∠𝐵𝑂𝐶= 38 𝑜 , 𝑚∠𝐴𝑂𝐵= 41 𝑜 𝑚∠𝐵𝑂𝐶= 41 𝑜 , 𝑚∠𝐴𝑂𝐵= 38 𝑜 𝑚∠𝐵𝑂𝐶= 28 𝑜 , 𝑚∠𝐴𝑂𝐵= 51 𝑜 𝑚∠𝐵𝑂𝐶= 51 𝑜 , 𝑚∠𝐴𝑂𝐵= 28 𝑜 Non-Response Grid

The answer is A. 𝑚∠𝐵𝑂𝐶= 38 𝑜 , 𝑚∠𝐴𝑂𝐵= 41 𝑜 If 𝑚∠𝐴𝑂𝐶= 79 𝑜 , 𝑚∠𝐵𝑂𝐶=2𝑥+10, and 𝑚∠𝐴𝑂𝐵=4𝑥−15, find the degree measure of∠𝐵𝑂𝐶 and ∠𝐴𝑂𝐵. The diagram is not to scale. 𝑚∠𝐴𝑂𝐶=𝑚∠𝐴𝑂𝐵+𝑚∠𝐵𝑂𝐶 79=4𝑥−15+2𝑥+10 79=6𝑥 −5 84=6𝑥 14=𝑥 2 14 +10=38 4 14 −15=41

20. If EF = 14 and EG=33, find the value of FG 20. If EF = 14 and EG=33, find the value of FG. The drawing is not to scale. 19 14 18 21 Non-Response Grid

The answer is A. 19 If EF = 14 and EG=33, find the value of FG. The drawing is not to scale. 𝐸𝐹+𝐹𝐺=𝐸𝐺 14+𝐹𝐺=33 𝐹𝐺=33−14=19 𝐹𝐺=19