8.04 Geometry Unit Exam

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8.04 Geometry Unit Exam

Question 1

  1. The opposite angles of a parallelogram are congruent.

2 points

Question 2

  1. In a rectangle, the opposite sides are congruent.

2 points

Question 3

  1. If a parallelogram is a rectangle then the diagonals are congruent.

2 points

Question 4

  1. The following is a rhombus, therefore angle CDA is congruent to angle BDA
    parallelogram ABCD with diagonals BD and AC

2 points

Question 5

  1. If a quadrilateral is a kite, then its diagonals bisect each other.

2 points

Question 6

  1. ABCD is a parallelogram. If AE is equal to one-half b plus 1 and EC is equal to b – 15, find the measure of AE.
    parallelogram ABCD with diagonals BD and AC that cross at point E

    Question 7

    The diagonals of rhombus FGHJ intersect at point K. If side GK is equal to 3x – 5 and side JK is equal to 4x – 8, find x.

    Question 8

    A rectangle ABCD has the following sides. Find x and y.
    rectangle ABCD, side AB measures y, side BC measured y minus x, side CD measures 3 and side DA measures 4

    Question 9

    ABCD is a parallelogram. If angle B is equal to (2x)° and angle A is equal to (-x + 120)°, find x.
    parallelogram ABCD

    Question 10

    ABCD is a parallelogram. If AB is equal to 2x + 1 and CD is equal to x + 13, find x.
    parallelogram ABCD with diagonals BD and AC that cross at point E

    Question 11

    Triangle ABC and DEF are congruent. Find x.
    triangle ABC, side AB measures x plus 6, side BC measures x, side CA measures x plus 4, triangle DEF, side DE measures 3 x minus 5

    Question 12

    Triangle ABC is congruent to triangle DFE. Find x.
    triangle ABC, side AB measures 10, side BC measures 20 and side CA measures 12, triangle DFE, side EF measures x minus 13

    Question 13

    Triangle RSV is congruent to triangle TVS. Find x and y.
    triangle RSV similar to triangle TVS, side RS measures y, side RV measure 1, side TV measures negative x plus 4 and side ST measures 4 x minus y

    Question 14

    Triangle ABC is congruent to triangle DFE. Find x.
    triangle ABC, angle A equals 33 degrees, angle B equals 100 degrees and angle C equals 47 degrees, triangle DFE, angle F equals 2 x plus 1 degrees

    Question 15

    Triangles QVS and RTS are similar. Find side VS.

    triangle QVS similar to overlapping smaller triangle RTS, segment QV equals 16, segment VS equals x, segment RT equals 8 and segment TS equals 20

    Question 16

    Triangles WSR and TVR are similar. Find x.
    triangle WSR similar to larger triangle TVR, segment WS equals 8, segment RW equals x plus 8, segment TV equals 12 and segment RT equals x plus 14

    Question 17

    Triangle ABE is similar to triangle ACD. Find y.
    triangle ABE similar to larger triangle ACD, segment AB equals 4, segment AC equals 6, segment BE equals x, segment AE equals y, segment ED equals 7 and segment CD equals 3

    Question 18

    Triangles MOP and MNQ are similar. Find x.
    triangle MOP similar to smaller triangle MNQ, segment MQ equals 15, segment QP equals x, segment MN equals 12 and segment NO equals 5

    Question 19

    Find x.
    circle S with inscribed triangle PQR, side PR goes through point S, side PQ is congruent to side QR, angle P equals 6 x minus 6 degrees, angle R equals x plus 9 degrees

    Question 20

    Find x.
    circle S with inscribed triangle PQR, side PR goes through point S, side PQ is congruent to side QR, angle P equals x minus 10 degrees, angle R equals 2 x plus 10 degrees

    Question 21

    Point C is the center of the circle. Angle ACB measures 56 degrees What is the measure of arc AB?
    circle C with central angle ACB and point D on the major arc

    Question 22

    Point C is the center of the circle. What is the measure of angle ACB if arc ADB measures 250 degrees ?
    circle C with central angle ACB and point D on the major arc

    Question 23

    Point C is the center of the circle. What is the measure of arc AB if angle ACB is equal to 80 degrees ?
    circle C with central angle ACB

    Question 24

    Point C is the center of the circle. What is the measure of arc ADB if angle ACB is equal to 102 degrees ?
    circle C with central angle ACB and point D on the major arc

    Question 25

    Angle C is an inscribed angle of circle P. Angle C measures x plus 8 degrees and arc AB measures (-8x) negative 8 x degrees . Find x.
    circle P with inscribed angle ACB

    Question 26

    Point C is the center of the circle. If angle ACB measures
    4 x plus 12 degrees and AB measures (x + 13) x plus 13 degrees , find x.
    circle C with central angle ACB and point D on the major arc

    Question 27

    Circles M and K are congruent, arc QR is congruent to arc LN . Find the length of segment QR .
    circle M with chord QR, measuring 4 x minus 10, circle K with chord LN measuring 2 x plus 2

    Question 28

    Circles M and K are congruent, arc QR is congruent to arc LN and arc OP is congruent to
    arc VW . Find x and y.
    circle M with chord QR, measuring x plus 5, circle K with chord LN measuring 2 x plus 10

    Question 29

    Circles M and K are congruent, arc QR is congruent to arc LN and arc OP is congruent to
    arc VW . Find x and y.
    circle M with chord QR, measuring x plus 2 and chord WV measuring y, circle K with chord LN measuring y and chord PO measuring 2x minus 1

    Question 30

    Circles M and K are congruent, arc QR is congruent to arc LN and arc OP is congruent to
    arc VW . Find x and y.
    circle M with chord QR, measuring 8 and chord WV measuring 2 x, circle K with chord LN measuring 3 x plus 4 y and chord PO measuring 5 y minus 3

    Question 31

    Find the measure of arc BC if angle A is equal to 18 degrees and measure of arc DC measures 48 degrees .
    circle with points B, C and D on the circle, point A outside the circle, line ABC through the circle and line AC tangent to the circle

    Question 32

    Segment AB and segment BC are tangent to circle D. Find x if Segment AB = segment BC and segment BC = 7. Find x. circle D with points A and C on the circle, point b outside the circle, segments BA and BC are tangent

    Question 33

    Segment AB and segment BC are tangent to circle D. Find x if Segment AB = -x + 6 and segment BC = 3x + 1. Find x.
    circle D with points A and C on the circle, point b outside the circle, segments BA and BC are tangent

    Question 34

    Find x.
    circle with points A, B, C, and D on the circle, segments AC and BD crossing at point E inside the circle, arc BC is 65 degrees, arc AD is 80 degrees and angle BEC is x degrees

    Question 35

    Find angle A if measure of arc DE is equal to 23 degrees and measure of arc BC is equal to 15 degrees .
    circle with points B, C, D and E on the circle, point A outside the circle, line ABC through the circle and line ACE through the circle

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