Euclidean Geometry

7) In parallelogram SNOW, ST = 6, NW = 4, m∠OSW=36°, m∠SNW=58°, and m∠NTS=80°.

a) Find SO.

b) Find NT.

c) Find m∠NWS.

d) Find m∠SOW. 7)

a)

b)

c)

d)

8) Find the value of x and y that would make the quadrilateral a parallelogram.

8)

9) Determine what type of quadrilateral ABCD has given the coordinates: A(1, −1), B(7, 1), C(8, −2), D(2, −4). Show work and justify your reasoning.

9)

10) Complete the proof.

Given: ABCD is a rectangle W, X, Y, and Z are midpoints of BC, AB, AD, and CD respectively

Prove: quadrilateral WXYZ is a rhombus

STATEMENTS REASONS

ABCD is a rectangle. Given

(BW) ̅≅(WC) ̅, _________, _________, _________ Definition of Midpoint

BD = AC

(XY) ̅ is a midsegment in ∆ABD,

_________________, ________________ Definition of a Triangle Midsegment

XY = ½ BD = WZ and ________________ The midsegment of a triangle is equal to one-half the length of the parallel side.

½ BD = ½ AC

XY = WZ = YZ = XW

WXYZ is a rhombus

11) Find x and y. Simplify all radicals – do not use decimal approximations.

11)

12) Find x.

12)

13) The two figures are similar. Find x.

13)

14) Determine whether the quadrilaterals are similar. If so, write the similarity statement.

14)

15) Determine whether the triangles are similar. If so, write the similarity statement and theorem (SSS, SAS, or AA).

15)

16) Determine whether the triangles are similar. If so, write the similarity statement and theorem (SSS, SAS, or AA).

16)

17) Determine whether the following triangles are acute, obtuse, or right.

a) 48, 55, 76

b) 20, 20, 24

c) 5, 12, 15

17)

a)

b)

c)

18) Find the missing sides.

18)

19) Find the missing sides.

19)

20) Find x.

20)

21) Find x.

21)

22) Find the measure of angle x.

22)

23) Find the measure of angle x.

23)

24) Use the Law of Sines or Law of Cosines to solve the triangle. Round answers to the nearest tenth.

24)

25) Find x.

25)

26) Find x.

26)

27) Solve for x if PQ = x + 7 and PR = 2x – 9.

27)

28) Find x.

28)

29) The area of a parallelogram is 15 in.2. If the base is 5 in., what is the height?

29)

30) Find the area of a circle whose diameter is 34 cm.

30)

31) Find the surface area and volume.

32) Find the surface area and volume.

32)

33) Find the area of the blue sector.

33)

34) The vertices of ∆GHI are G(1, 1), H(5, 1), and I(5, 4). Reflect ∆GHI over the x−axis. Find the coordinates of △G′H′I′.

34)

35) The vertices of ∆ABC are A(−6, −7), B(−3, −10), and C(−5, 2). Find the vertices of ∆A′B′C′, given the translation rule: (x, y) → (x − 5, y + 8)

35) For more information on Euclidean Geometry check on this: https://en.wikipedia.org/wiki/Euclidean_geometry

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