Geometry Quarter 2 Study Packet

Quarter 1 Important Vocabulary Parallel, Perpendicular, Perpendicular Bisector, Acute, Right, Obtuse, Straight angle, Scalene, Isosceles Equilateral, Triangle, Exterior Angle, Vertical Angles, Supplementary, Complementary, Median, Altitude, Alternate Interior Angles, Alternate Exterior Angles, Same Side Interior Angles, Same Side Exterior Angles, Corresponding Angles, Midpoint, Bisector, Right Angle, Hypotenuse, Adjacent Angles

Quarter 2 Important Vocabulary Congruent, Reflexive Property, Transitive Property, Substitution, SAS, ASA, SSS, AAS, Hy-Leg, CPCTC, Pre-image, Image, Translation, Rotation, Reflection, Map, Rigid Motion, Preserved, Parallelism, Symmetry (Line, Point and Rotational), Orientation, Series of rigid motions

Quarter 1 Review – chapters 1-3

1. Given: AE bisects ∠DAB . Find ED if CB = 12 and CE = 16. (not drawn to scale) (1) 20 (2) 4 (3) 28 (4)192 2. In the figure shown, ∠m AED = 117. Which of the following statements is false?

(1) ∠m BEC = 63 (2) ∠BEC and ∠CED are adjacent angles (3) ∠AEB and ∠DEC are vertical angles (4) ∠m AEB = 63

3. Two parallel roads, Elm Street and Oak Street, are crossed by a third, Walnut Street, as shown in the accompanying diagram. Find the number of degrees in the acute angle formed by the intersection of Walnut Street and Elm Street.

Name:____________________________________________________________  

 

 

4. In a right triangle the hypotenuse is 10 inches and one of the legs measures 4 inches. Determine the measure of the other leg in simplest radical form.

5. In the diagram of below, and . Line segment MS connects

points M and S on the triangle, such that . What is ?

(1) 163 (2) 121 (3) 42 (4) 17

6. The degree measures of the angles of are represented by x, 3x, and . Find the value of x.

7. In the diagram below of , side is extended to point D, , , and . What is ?

(1) 5 (2) 20 (3) 25 (4) 55

8. Match each definition below to its corresponding picture.

Altitude Angle Bisector Median Perpendicular Bisector

Chapter 4 Review – Intro to Proofs

9.  Which  of  the  following  is  an  example  of  the  reflexive  property?  (1)    𝑀𝐻 ≅ 𝑀𝐻                                          (2)    𝐴𝐵  +  𝐵𝐶  ≅ 𝐴𝐶            (3)  the  measure  of  the  angles  in  ∆ABC  =  180°      (4)    if  a  =  b  and  b  =  c,  then  a  =  c      10.    Which  of  the  following  statements  could  be  used  to  prove  𝐽𝐾  is  a  median  of  ∆MJL?  (1)    𝐽𝐾  ⊥  𝑀𝐿             (2)    𝐽  lies  on  side    𝐽𝑀  (3)    𝐾  is  the  midpoint  of  𝑀𝐿             (4)    𝐽𝐾  bisects  ∠𝑀𝐽𝐿      11.      Which  of  the  following  could  not  be  used  to  prove  a  pair  of  angles  are  congruent?  (1)  a  segment  is  an  angle  bisector     (2)  a  pair  of  angles  are  vertical  angles  (3)  a  pair  of  angles  are  right  angles     (4)  a  pair  of  angles  are  supplementary      12.    Which  of  the  following  can  be  used  to  prove  two  lines  are  parallel?  (1)  same  side  interior  angles  are  supplementary  (2)    same  side  interior  angles  are  congruent    (3)  corresponding  angles  are  supplementary  (4)  corresponding  angles  are  complementary      13.  Given  𝐺𝑃𝐻  intersects  𝐴𝑃𝐵  at  P,  m∠𝐺𝑃𝐴  =  (2x  +  40)°,  and                m∠𝐴𝑃𝐻  =  (3x  +  60)°,  explain  why  m∠𝐵𝑃𝐻  =  72°.          Use  appropriate  geometry  vocabulary.            14.    Lines  𝑚  and  𝑛  are  parallel.  If  m∠1  =  58°  and  m∠4  =  46°,          explain  why  m∠5  =  76°.  Use  appropriate  geometry  vocabulary.              15.      Given  𝐽𝐾 ≅ 𝐿𝑀                Prove:  𝐽𝐿 ≅ 𝐾𝑀                

J K L M

16.      Prove  the  exterior  angle  theorem  (m∠4  =  m∠2  +  m3)      

     Statement               Reason    1.  m∠1  +  m∠2  +  m∠3  =  180             1.  _____________________    2.    ____________________               2.  Linear  pairs  a  supplementary      3.    m∠2  +  m∠3  -­‐  m∠4  =  0             3.  _____________________    4.  _____________________             4.  Reflexive  Property    5.  _____________________             5.  Addition  Property    Chapter 5 Review – Triangle Proofs

17. In the diagram of and below, , , and .

Which method can be used to prove ?

1) SSS 2) SAS 3) ASA 4) HL

18. Which condition does not prove that two triangles are congruent?

1) 2) 3) 4)

19. In the accompanying diagram of triangles BAT and FLU, and .

Which statement is needed to prove ?

1) 2) 3) 4)

20. If and is the shortest side of , what is the shortest side of ?

1) 2) 3) 4)

21. If , which statement is always true?

1) 2) 3) 4)

22. In the diagram of quadrilateral ABCD, , , and diagonal is drawn.

Which method can be used to prove is congruent to ?

1) AAS 2) SSA 3) SAS 4) SSS

23. In the diagram below, line p intersects line m and line n.

If and , lines m and n are parallel when x equals

1) 12.5 2) 15 3) 87.5 4) 105

22. Given: , , , ,

Prove:

23. Given: BC is an altitude of ΔABD

BC bisects ∠ABD

Prove: ΔACB ≅ ΔDCB

Chapter 6 review – rigid motions

24.  Which  of  the  following  would  map  𝐴𝐵𝐶𝐷  to  ′𝐵′𝐶′𝐷′  ?  (1)    A  rotation  of  90°  followed  by  a  translation  3  units  left  (2)  A  reflection  over  the  y-­‐axis  followed  by                a  translation  of  3  units  up  (3)  A  reflection  over  the  line  𝑦 = 𝑥  followed  by  a              a  translation  of  3  units  down  (4)  A  rotation  of  90°  followed  by  a  reflection  over  the  x-­‐axis      25.  The  image  of  ∆ADF  after  a  reflection  over  𝐹𝐸  followed  by    a  reflection  over  𝐻𝐺  is  (1)  ∆𝐻𝐺𝐵   (2)  ∆𝐵𝐶𝐺       (3)  ∆𝐹𝐸𝐺   (4)  ∆𝐷𝐸𝐹        26.  Which  of  the  following  could  be  used  to  justify  why  ∆𝐴𝐵𝐶   ≅  ∆𝐴!!𝐵!!𝐶′′  ?    (1)      ∆𝐴𝐵𝐶    and    ∆𝐴!!𝐵!!𝐶′′  have  the  same  area  (2)      𝐴𝐵 ≅ 𝐴′𝐵′  and  𝐵𝐶   ≅ 𝐵′𝐶′  (3)    The  same  line  is  the  perpendicular  bisector  of    𝐵𝐵′′  and  𝐶𝐶′′  (4)    A  single  translation  that  maps  𝐶  to  𝐶′′  and  𝐵  to  𝐵′′,  followed              by  a  reflection  over  𝐵′′𝐶′′  that  maps  𝐴  to  𝐴′′.    27.  Which  of  the  following  transformations  would  not  map  the  given  point  onto  itself?    (1)  Point  𝐾  is  reflected  over  a  line  that  passes  through  𝐾  (2)  Point  𝐶  is  rotated  by  90°  about  point  C  (3)  Point  A  undergoes  the  translation  𝑇!,!  (4)  Point  D  is  rotated  360°  about  the  origin      28.  Point  𝐷′(4,  10)  is  the  image  of  point  𝐷(7,  8)  after  a  translation.  What  is  the  image  of  point  Q(3,  1)  after  the  same  translation.  (1)  (0,  3)         (2)    (6,  -­‐1)     (3)    (10,  9)     (4)      (4,  7)        29.  Point  Q  has  coordinates  (-­‐4,  7).  Find  the  coordinates  of  each  of  the  following:      a)    R90°               c)    rx  =  5  ∘  T3,6          b)  ry=x                 d)  ry-­‐axis  ∘  R270°      30.  𝑆𝑇  is  the  perpendicular  bisector  of  𝑀𝐽  ,  𝑁𝐾,  and  𝑂𝐿.  What  can  you  conclude  about  ∆𝑀𝑁𝑂  and  ∆𝐽𝐾𝐿.  Explain  your  reasoning.    

31.  Determine  the  transformation  that  produced  the  following  images:     a)             b)            `                

32.    Point  𝑉  is  the  midpoint  of  segment  𝐶𝑆.  If  the  coordinates  of  𝐶  are  (3,  1)  and  the  coordinate  of  𝑉  are  (5,  4).  Identify  the  following  translations:  

a)  the  translation  that  will  map  𝑉  to  𝑆       b)  the  translation  that  will  map  𝐶  to  𝑆  

     33.  Graph  the  coordinate  axes  below,  graph  the  following:    a)    ∆𝐽𝑂𝐵  with  coordinates  J(2,  1)  O(6,  3)  B(1,  5).    b)  ∆𝐽′𝑂′𝐵′,  the  image  of  ∆𝐽𝑂𝐵  after  a  reflection                  over  the  line  y  =  -­‐1    c)  ∆𝐽′′𝑂′′𝐵′′,  the  image  of  ∆𝐽′𝑂′𝐵′  after  a                  rotation  of  180°                          34.  In  the  accompanying  figure,  𝐴𝐷 ≅ 𝐵𝐹 ≅ 𝐶𝐸    

and  𝐴𝐷 ≅ 𝐶𝐸 ≅ 𝐵𝐹.  Explain  why  w𝐵𝐶 ≅ 𝐸𝐹.          

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x

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y

x

F

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D

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