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Geometry H
Section 10/1-10/4 Review worksheet answers
P is the center of the circle.
ABC is a tangent at point B.
17x + 20 = 360
17x = 340
x = 20
5. If the measure of BPK is 32, find the
measure of arc BML.
By the Arc Addition Postulate, the measure of
arc BML equals the measure of arc BK plus
the measure of arc KML.
The measure of arc BK is 32 because the
measure of central angle BPK is 32.
The measure of arc KML is 180 because it is
a semicircle.
So the measure of arc BML is 32+180, or
212.
1. If PB = 15, KL = ___
Q is the center of the circle.
GH  IJ
If PB = 15, then PJ = 15 and PK = 15.
So, KL = 15 + 15 = 30
2. If AP = 5 and AB = 3, PJ = ___
Because of the tangency, ABC is a rt. .
(PB)2 + (AB)2 = (AP)2
(PB)2 + (3)2 = (5)2
(PB)2 + 9 = 25
(PB)2 = 16
PB = 4
Since they are both radii, PB = PJ.
So, PJ also equals 4.
3. If mJPK = 80, find the measures
of arc JBK and arc JLK.
If mJPK = 80, then the measure of arc JBK
is also 80.
Since arc JLK is the minor arc of arc JBK, its
measure is 360 – 80, or 280.
4. The measure of arc JL = 6x and the
measure of arc JKL = 11x + 20. Find x.
A minor arc and its major arc always add up
to 360.
6x + (11x + 20) = 360
6. The measure of arc GH is 65. Find the
measure of arc ISJ.
Since GH  IJ , arc GH and arc IJ are
congruent.
So the measure of arc IJ is also 65.
Arc ISJ is the major arc of minor arc IJ.
So, the measure of arc ISJ is 360 – 65, or
295.
Geometry H
Section 10/1-10/4 Review worksheet answers
7. The distance from Q to GH is x2 + 4x - 2.
Z is the center of the circle.
The distance from Q to IJ is 12 – x.
Find x.
Since they are congruent chords, they are
equidistant from the center.
x2 + 4x – 2 = 12 – x
x2 + 5x – 14 = 0
(x + 7)(x - 2) = 0
x = -7 or x = 2
8. If SV = y + 4 and ST = 6y, find VT.
Since QU  ST , QU bisects ST .
Because V is the midpoint of ST ,
ST = 2∙SV
6y = 2(y + 4)
6y = 2y + 8
4y = 8
y = 2
Since y = 2, SV =6. Therefore VS = 6.
11. If the measure of arc NS = 70,
mNMS = ____
Since NMS is an inscribed angle, its
measure is half the measure of the arc it
intercepts. Half of 70 is 35.
9. QU = 10. ST = 16. Find VU.
Since they are both radii, QS = QU = 10.
Since ST = 16 and V is the midpoint, SV = 8.
In rt.  QVS,
(QV)2 + (SV)2 = (QS)2
(QV)2 + (8)2 = (10)2
(QV)2 + 64 = 100
(QV)2 = 36
QV = 6
By Segment Addition Postulate,
QV + VU = QU
6 + VU = 10
VU = 4
10. The measure of arc SIT = 240.
Find the measure of arc SU.
If the measure of major arc SIT = 240,
the measure of minor arc SUT = 120.
Since a radius perpendicular to a chord bisects
both the chord and its minor arc, the measure
of arc SU must be 60.
12. If mMZT = 48, mMST = ___
Since MZT is a central angle, the measure
of its minor arc, arc MT, must also equal 48.
The measure of the inscribed angle, MST, is
half the measure of the arc it cuts off, arc MT.
mMST = 24.
13. Find TMS.
Since TMS is inscribed in a semi-circle
(arc TNS), its measure must be 90.
14. If mNMS = 28, find the measure of
arc TMN.
The measure of arc TMN plus the measure of
arc NMS equals the measure of arc TNS, a
semi-circle. Since measure of arc NMS
equals 56 (twice the measure of NMS) and
the measure of arc TNS equals 180, then the
measure of arc TMN equals 180 - 56, or
124.
Geometry H
Section 10/1-10/4 Review worksheet answers
Quad. ABCD is not drawn to scale.
18. If BD is a diameter, AD = 12,
and AB = 5, find DB.
If BD
(DB)2
(DB)2
(DB)2
(DB)2
DB
is a diameter, DAB is a right angle.
= (DA)2 + (AB)2
= (12)2 + (5)2
= 144 + 25
= 169
= 13
19. If ABCD is a parallelgram,
what type of parallelogram is it?
In a parallelogram, opposite angle are
congruent.
15. If mD = 38, mB = ____
For a quad. inscribed in a circle opposite
angle must be supplementary.
mB = 180 – 38 = 142
16. If A is right angle, what other angle
or angles must be a right angle?
Since A and C are supplementary,
whenever mA = 90, mC = 90.
17. If arc AB is congruent to arc BC
and arc AD is congruent to arc DC,
what type(s) of quad might ABCD be?
A and C would be both congruent and
supplementary and therefore be right angles.
B and D would be both congruent and
supplementary and therefore be right angles.
A parallelogram with four right angles is a
rectangle. (It might or might not also be a
square.)
20. Which of the following could ABCD
not be?
A. isosceles trapezoid
B. non-isosceles trapezoid
C. rectangle
If arc AB is congruent to arc BC
and arc AD is congruent to arc DC,
then AB  BC and AD  DC .
D. non-rectangular parallelogram
If AD  AB , then all four sides are
congruent, and it’s a rhombus.
F. non-square rhombus
If AD is not congruent to AB , then there
are exactly two pairs of consecutive sides
congruent, and it’s a kite.
E. square
G. kite
B. In a non-isosceles trapezoid, opposite
angles are never supplementary.
D. By problem 19, if ABCD is a
parallelogram, then it must be a rectangle.
F. A rhombus is a parallelogram. By
problem 19, if ABCD is a parallelogram, then
it must be a rectangle. If it’s not a rectangle,
then it’s not a square.