2. Find the unknown side length of the right triangle. Write your answer in simplest radical form and decimal form. (7.1) I -- ' t ) "-" "

Transcription

1 Name: () ÿ!ÿ.ÿ,ÿ... MDL Geometry Chapter 7: Date: Period: Spring Semester Review - Part 1 Chapters 7 & 8 1. What is the Pythagorean Formula?(7.1) 2. Find the unknown side length of the right triangle. Write your answer in simplest radical form and decimal form. (7.1) I /, >I :,ÿ? zo 15,ÿ3 F IcY- -. /" 3. Defetÿmine if-the given measures are measures of the sides of a right triangle. (7.2) h\ty, ' )L.,ÿ " cj 15, 36, 39 21, 72, 75 24, 46, 51 ks ") <2 I"'ÿ,) ' t ) "-" " I ji,! ; Find the geometric mean of 40 and 10. (7.3) _cÿ,.(<?? 5. Find the geometric mean of 6 and 9. (7.3)G "\ ÿi} '?>I i 6. Find the value of x. Round your answers to the nearest tenth. (7.3) 6 jjl I x 2O 25 <- (ÿ-' jtÿ,' /'. i i!-,) ) (ÿ) i,,

2 7. Find the missing measures. Write your answers in simplest radical form. (7.4) 9 8. Classify the triangles formed by the side lengths as acute, right, or obtuse. (7.2) x (D) 13, 18, ) J,(ÿ5ÿ ÿ1 ) Matchins: (7.5 & 7.6) Lÿ 9. sin of an angle opposite (A) adjacent (ÿ cos of an angle (B) opposite hypotenuse 11. tan of angle (C) adjacent hypotenuse 12. Find the sine, cosine, and tangent of angle A in A ABC. Put answers in fraction form and reduce if needed. (7.5 & 7.6) /9. ÿ-ÿ A (A) The sine (sin) of angle A in AABC isÿ)::) =,tÿ- (B) The cosine (cos) of angle A in AABC is ÿ.;) -- <... (C) The tangent (tan) of angle A in AABd is ÿ = ' i ' L A 50-meter vertical tower is braced with a cable secured at the top of the tower. The cable forms a 31 angle with the tower. How far is the cable tied from the base of the tower? (7.5 & 7.6) l "... ÿ.i ) ( (fl ÿ' ÿ /'ÿ " <' i :,+... :{ > +' ÿl<i (Y)! ' i ÿ i '

3 14. A 16-foot ladder leaning against a building forms a 21 o angle with the side of the building. How far is the base of the ladder from the base of the building? (7.5 & 7.6) Chapter 8: <', 15. Give the names for each polygonwith the given number of sides: (8.1) 3 sides / 0 h o[ td:!ÿ 7 sides 4 sides / ÿiiÿ#i ÿ, I I f 5 sides t/1, 6 sides 16. Find the following for a regular hexagon:(8.1) (A) The interior angle sum (B) The measure of each interior angle The exterior angles sum (D) The measure of each exterior angle 3 d7... //" // 17. Find the following for a regular 19-gon:(8.1) (A) The interior angles sum (l i ÿ/ÿ) (B) The measure of each interior angle (C) The exterior angles sum : i (D) The measure of each exterior angle

4 18. Put an X in the box if the shape always has the given property. ( ) Property All sides are congruent Both pairs of opposite sides are congruent Both pairs of opposite sides are parallel Exactly one pair of opposite sides are parallel Parallelogram / Rectangle i' 11i Rhombus / Square / Kite Trapezoid f All angles are congruent Exactly one pair of opposite angles are congruent,f j J- Diagonals are perpendicular + +, Diagonals are congruent Diagonals bisect each other,/f,/ 19. Given the following combinations of calculations, which figures can you identify? (8.6) Distance formula only Slope formula only Either distance or slope Both distance and slope are required Parallelogram,f Rectangle Rhombus Square Trapezoid,J

5 Name: MDL Geometry Date: Spring Semester - Part 2 Chapters 9 & 10 Period: Chapter 9: 1. Identify the three isometries: ( ) 2. What transformation is not an isometry? (9.7) 3. The vertices of A ABC are A(2, 3), B(1, 0), and C(-2, 4). Graph the image of A ABC after the translation (x, y) -ÿ (x 3, y - 2). (9.1)... I 6 Cÿ L JL.LoL3C]ÿ,_,.oi Graph the reflection of the polygon in the given line. (9.3),!ÿ,/ X= i; ' i _ÿ_ f- I i I i I i t '\ if'

6 5. Intentionally skipped. 6. Determine whether the following dilations are an enlargement, reduction, or congruent transformation based on the given scale factor: (9.7) (A) k -7ÿ)t! (m k= I!7ÿ ;t... t 3,.ÿ iÿ- (C) k=- 2 s,t Chapter 10: For # 7-16, the segment, ray, or line (using proper notation) that best describes the given part of the circle. (10.1).ÿJ-I- (_:ÿ> 7, Center /-> soca=t 9. iameter 17. If the measure of an arc is less than 180 ' then the arc is aÿÿu arc. (10.1) If the measure of an arc is greater than 180, then the arc is a [ÿ("ÿtgjÿ ÿ ()7,3 arc. (10.1) 19. If the measure of an arc is equal to 180, then the arc isa - "- ' " " ÿ.(10.1) 20. The opposite angles in an inscribed quadrilateral are -" '- "ÿ.... (10.4) 21. The circle is circumscribed by the pentagon as shown. If AB = 10, BC = 5, AI = 14, GF = 6, and GE = 12. Find the following measures: (10.1) Cb = ÿ be = )& I4_G = Perimeter =

7 22. Find the value of x. (10.1) A -- io 23. Find the radius of the circle. (10.1)... ;.0 lÿ-iq -i'lo ÿ-r '> { 24. Find the measure of arc AC. (10.4) f Find the m < 1. (10.5) 238ÿ 26. Find the m < ABC. (10.4) I06ÿ, f:1ÿ 1, i +ÿ.,0... ÿ'7. { 27. Find the measure of arc ABC. (10.4) > A /..-" k B <<4 3ÿ_ 1,---- <>,( f> f<,- "I...,# o 28. Find the m < 2. (10.5) /\ -"'-K '\ /..%Z /!SZ. ±... <C2 '-'ÿ o "\,,

8 ) ') f g (. XJ:<.ÿ).:,. 1'<;) I.i many common tangents do the two circles share7 (10.1) 34. Find the value of x and y. 36. Find KD. 37. Given: O, AC = 24. Find BD. D % # o....

9 Name: MDL Geometry / k ft ÿ fs Date: Period: Spring Semester Review - Part 3 Chapters 11 & 12 Chapter 11: For # 1-6, write the Area formula for the following polygons: (11.1, 11.2, 11.6) 1. Triangle Parallelogram lpezoid 4 Rhombus, Kite I, Regular Polygon For # 7-12, find the area Of each polygon. Round answers to the nearest tenth. (11.1, 11.2, 11.6) 8 9 t5m \ t0. ti 40in--t 13. If two figures are similar and the ratio of sides lengths is a:b, then the ratio of perimeters is and the ratio of areas is O'ÿ ÿ J:;,'>. (11.3)

10 14. Thecorresponding sides. (11.3)rati of areas of two similar figures,ÿ)ÿiÿ ÿ 144:4ÿri_. ':'- Iÿ(ÿte the ratio of the lengths of the 15. Two triangles are similar. The smaller triangle has a side length of 4, while the larger has a side length of 10. If the area of the larger triangle has an area of 200, what is the area of the smaller triangle. (11.3) ÿi [ÿ... ;Zÿ 2ÿ ÿ. ÿ.ÿ:ÿ I You have a great photo that is 3" by 5". You want to enlarge the area of the picture using a scale factor of 3. (11.3) "ÿ ÿ ÿ ÿ ÿj ÿf A) What is the area of the larger pjctur.l,ÿ,ÿ.:.ÿ ÿ Jr?... ÿ ]ÿ B) Will it fit on your 9 x 12 scrapbook page? Find the exact and approximate circumference of a circle with a diameter of 50 inches. (11.4) Exact: _ÿl!ÿ(iiiÿ ]ÿf J/ÿ Approximate:ÿ O. 0"ÿÿ //'ÿ Formulas for Circles: Area = ÿr2 Circumference = 2ÿr or ÿa' Af Length of an arc = --. 2m- 360 Area of a Sector = -- For # 18 & 19, find the indicated measure. (11.4),_f-.... (/' 18. Radius of circle F. t;ÿ tc> ÿ}ÿ 19. H 20. Find the length of arc Cb with an arc measure o:.!08 ond.a radius of 17 cm, (!1.!!_ÿÿ

11 For # 21 & 22, find the indicated measure. (11,5) 21. The area of the farmed by ÿ QSR., Area of the circle 23. Find the area of a sector with an arc measureo[,!ÿ14 anti, radius of 10 in. (11.5) ;o I {:)ofl l A point K is serected randomly on AC. What is the probability that K iÿ on AB? (U.7) O 25. What is the probability that the arrow will land in sector 5? Express your answers as a fraction and as a decimal, (11.7)

12 Chapter 12: (i )If I'4/)ÿ'ÿ 26. Draw the nets for the solids below. (12.1) Pentagonal Prism Pentagonal Pyramid \ For # 27-31, write the Lateral Area, Surfac Volume formulas for each solid. ( ) 27. Prism: LA = ÿ SA : v: 28. Cylinder: 29. Pyramid: i V= t Ix, 30. Cone: 31. Sphere SA: U,Iÿ!)(''2 V= For # 32-35, find the LA, SA, and Volume of each solid. Pictures are not necessarily drawn to scale. 32. Square Pyramid (12.5) LA : SA : V:

13 33. Rectangular P!ism (12.2) 9 /]t- '...! / 8in SA ÿ L v. ÿsiÿ' // i... I loin. 34. Right Cone (12.5) l 15 7ÿ, y.- _. & I...,-,;!,l:s-ÿJAÿo) 24m / I,... "-.,,,, "?v7; " 5A--... /'}')... Vÿ! i Find the surface area and volume of a sphere with a radius of 16cm. (12.6) '2ÿ.;.5

14 37. The lateral area of a cylinder is If 657vin2. the radius is 5 in., find the height. (12.4)... + io... Height = 38. The surface area of a sphere is 256Jvm2. Find the radius. (12.6) 39. I Tell whether the pair of right solids is similar, congruent or neither. (12.7) II 16in loin 4,ÿm IBm d 40 Two similar cylindrical cans have a scale factor of 2:3. The smaller can has surface area 308 ÿv square inches and volume 735ÿv cubic inches. Find the surface area and volume of the larger can. 02.7) f4 V... ÿ SA = ÿ V = ly) 41 Find the surface area and volume of the triangular prism.,ÿ. SA= tÿ$,><tn c.ÿ17ÿ V= ÿ 7)' /)<l : J: ""....