# Geometry Review Packet

Semester 1 M.C. Final                               Name_______________________

Section 1.1

1.  Name all the ways you can name the following ray:             1________________________

Section 1.2

2.  What is a(n)

a)  acute angle                                                                        2a

b)  right angle                                                                         2b

c)  obtuse angle                                                                      2c

d)  straight angle                                                                   2d

3.  Change 41to degrees and minutes.

4.  Given:  ÐABC is a rt. Ð

mÐABD = 67°21’ 37”

Find:  mÐDBC

Section 1.3

5a.  AC must be smaller than what number?

5b.  AC must be larger than what number?

6.  Can a triangle have sides of length 12, 13, and 26?

7.  Given:  mÐ1 = 2x + 40

mÐ2 = 2y + 40

mÐ3 = x + 2y

Find:  mÐ1, mÐ2, and mÐ3

8.  is divided by F and G in the ratio of 5:3:2 from left to right.  If EH = 30, find FG and name the

midpoint of .

Section 1.4

9a.   Draw the reflection over

9b.  Draw the reflection over

Section 1.7

10.  What is a postulate?

11.  What is a definition?

12.  What is a theorem?

13.  Which of the above (#10 - 12) are reversible?

Section 1.8

14.  If a conditional statement is true, then what other statement is also true?

15.  State the converse, inverse, and contrapositive for the following conditional statement:

If Cheryl is a member of the Hinsdale Central basketball team, then she is a student at Hinsdale Central.

Converse:

Inverse:

Contrapositive:

16.  Place the following statements in order, showing a proper chain of reasoning.  Then write a

concluding statement based upon the following information:

a Þ b

d Þ ~c

~c Þ a

b Þ f

Section 2.1

1.  If  and Ð1, Ð2. and Ð3 are in the ratio 1:2:3, find the measure of each angle.

Section 2.2

2.  One of two complementary angles is twice the other.  Find the measures of the angles.

3.  The larger of two supplementary angels exceeds 7 times the smaller by 4°.  Find the measure of the

larger angle.

Section 2.5

4.  Given:  , GH = x + 10

HJ = 8, JK = 2x - 4

Find:  GJ

Section 2.6

5.  Given:  ÐHGJ ÐONP

and are bisectors

mÐHGJ = 25°, mÐONR = (2x + 10)°

Find:  x

Section 2.8

6.  Is this possible?

Section 3.2

1.   Name the method (if any) of proving the triangles congruent.  (SSS, ASA, SAS, AAS, HL)

a)                                                                                 b)

c)                                                                                 d)

e)                                                                                 f)

g)                                                                                 h)

2.  Identify the additional information needed to support the method for proving the triangles

congruent.

a)

DHGJ @ DOMK          by  SAS _______________

by ASA _______________

by HL ________________

b)                                                                    DPSV @ DTRV             by SAS _______________

by ASA _______________

by AAS _______________

c)                                                                     DZBW @ DXAY          by SSS _______________

by SAS _________________

Section 3.4

3.  Given:    is a median

ST = x + 40

SW = 2x + 30

WV = 5x – 6

Find:  SW, WV, and ST

Section 3.6

4.  If the perimeter of ΔEFG is 32, is ΔEFG scalene, isosceles, or equilateral?

5.  Given:   and  are the legs of isosceles ΔABC.

mÐ1 = 5x

mÐ3 = 2x + 12

Find: mÐ2

6.  If the mÐC is acute, what are the restrictions on x?

7.  Given: mÐ1, mÐ2, mÐ3 are in the ratio 6:5:4.

Find the measure of each angle.

8.  If ΔHIK is equilateral, what are the values of x and y?

Section 3.7

9.  Given: mÐP + mÐR < 180°

PQ < QR

Write an inequality describing the

restrictions on x.

10.  Given:   @

Solve for x.

Section 4.1

1.  Find the coordinates of the midpoint of each side of DABC.

Midpoint of AB =

Midpoint of BC =

Midpoint of AC =

2.  Find the coordinates of B, a point on circle O.

Section 4.3

3.  If squares A and C are folded across the dotted segments onto B, find the area of B that will not be covered by either square.

Section 4.6

5.  has a slope of .  If A = (2, 7) and B = (12, c), what is the value of c?

a.  Is  || ?

b.  Is  || ?

c.  Show that ÐR is a right angle.

7.  Given the diagram as marked, with  an altitude and  a median, find the slope of each line.

a.

b.

c.

d.  A line through A and parallel to .

Section 5.1

Use the diagram on the right for #1 & 2.

1.  Identify each of the following pairs of angles as alternate interior, alternate exterior, or corresponding.

a.  For and  with transversal ,

Ð1 and ÐC are _________________.

b.  For  and  with transversal ,

Ð2 and Ð4 are _________________.

2.  If  ||  is:

a.  Ð4 @ ÐC?                                    b.  Ð4 @ Ð3?                                    c.  Ð4 @ Ð2?

Section 5.2

3.  If Ð1 @ Ð2, which lines are parallel?

4.  Write an inequality stating the restrictions on x.

Section 5.3

5.  Are e and f parallel?

6.  Given:  a || b

mÐ1 =

mÐ2 =

mÐ3 =

Find:   mÐ1

7.  If f || g, find mÐ1.

8.  Given:   ||

Name all pairs of angles that must be congruent.

Sections 5.4 – 5.7

9.  ABCD is a      .

Find the perimeter of ABCD.

10.  Given:  mÐIPT = 5x – 10

KP = 6x

Find KT

11.  Given:        KMOP

mÐM =

mÐO =

mÐP =

Find:  mÐK

12.  Given:  RECT is a rectangle

RA = 43x

AC = 214x – 742

Find:  The length of  to the nearest tenth.

Sect. 6.1-6.2

1.   a Ç b = ________

2.  ET and point _______ determine plane b.

3.  M, E and T determine plane ________

4.   TE and  GM determine plane ________

5.   Name the foot of OR in a. ________

6.   Is M on plane b ? ________

7.   Given:  WY ^ XY

ÐWYZ = x + 68

ÐWYX = 2x – 30

Is WY ^ a ?

Sect. 6.3

8.   a.   Is ABCD a plane figure?

b.   If m || n, is AB || CD?

c.   If AB || CD, is m || n ?

9.  True or False.

a.   _____ Two lines must either intersect or be parallel.

b.   _____ In a plane, two lines ^ to the same line must be parallel.

c.   _____ In space, two lines ^ to the same line are parallel.

d.   _____ If a line is ^ to a plane, it is ^ to all lines on the plane.

e.   _____ Two planes can intersect at a point.

f.   _____ If a line is ^ to a line in a plane, it is ^ to the plane.

g.   _____ If two lines are ^ to the same line, they are parallel.

h.   _____ A triangle is a plane figure.

i.   _____  Three parallel lines must be co-planar.

j.   _____  Every four-sided figure is a plane figure.

Sect 7.1

1.   Given:    Ð5 = 70°

Ð3 = 130°

Find the measures of all the angles.

2.   Given:  Diagram as shown

Find:     AB and ÐW

3.   Find the restrictions on x.

4.   The measures of the 3 Ð’s of a D are in the ratio 2:3:5.  Find the measure of each angle.

5.   Given:   ÐT = 2x + 6

ÐRSU = 4x + 16

ÐR = x + 48

Find:  mÐT

Sect. 7.2

6.   Given: ÐA @ ÐD

B is the midpoint of CE

Is DABC @ DDBE?  If so, by which theorem?

7.   If ÐI @ ÐA, is ÐIFA @ ÐNLA ?

If so, by which theorem?

Sect. 7.3

8.   Find the sum of the measures of the angles in a 14-gon.

9.   What is the sum of the measures of the exterior angles of an octagon?

10.   Find the number of diagonals in a 12-sided polygon.

11.   Determine the number of sides a polygon has if the sum of the interior angles is 2340°.

Sect 7.4

12.  Find the measure of each exterior angle of a regular 20-gon.

13.  Find the measure of an angle in a regular nonagon.

14. Find the sum of the measures of the angles of a regular polygon if each exterior angle measures 30°.

Sections  1.1 - 7.4

Sometimes, Always or Never (S, A, or N)

___ 1.  The triangles are congruent if two sides and an angle of one are congruent to the corresponding

parts of the other.

___ 2.  If two sides of a right triangle are congruent to the corresponding parts of another right

triangle, the triangles are congruent.

___ 3.  All three altitudes of a triangle fall outside the triangle.

­­___ 4.  A right triangle is congruent to an obtuse triangle.

___ 5.  If a triangle is obtuse, it is isosceles.

___ 6.  The bisector of the vertex angle of a scalene triangle is perpendicular to the base.

___ 7.  The acute angles of a right triangle are complementary.

___ 8.  The supplement of one of the angles of a triangle is equal in measure to the sum of the other two

angles of the triangle.

___ 9.  A triangle contains two obtuse angles.

___ 10.  A triangle is a plane figure.

___ 11.  Supplements of complementary angles are congruent.

___ 12.  If one of the angles of an isosceles triangle is 60°, the triangle is equilateral.

___ 13.  If the sides of one triangle are doubled to form another triangle, each angle of the second

triangle is twice as large as the corresponding angle of the first triangle.

___ 14.  If the diagonals of a quadrilateral are congruent, the quadrilateral is an isosceles trapezoid.

___ 15.  If the diagonals of a quadrilateral divide each angle into two 45-degree angles, the quadrilateral

is a square.

___ 16.  If a parallelogram is equilateral, it is equiangular.

___ 17.  If two of the angles of a trapezoid are congruent, the trapezoid is isosceles.

___ 18.  A square is a rhombus

___ 19.  A rhombus is a square.

___ 20.  A kite is a parallelogram.

___ 21.  A rectangle is a polygon.

___ 22.  A polygon has the same number of vertices as sides.

___ 23.  A parallelogram has three diagonals.

___ 24.  A trapezoid has three bases.

___ 25.  A quadrilateral is a parallelogram if the diagonals are congruent.

___ 26.  A quadrilateral is a parallelogram if one pair of opposite sides is congruent and one pair of

opposite sides is parallel.

___ 27.  A quadrilateral is a parallelogram if each pair of consecutive angles is supplementary.

___ 28.  A quadrilateral is a parallelogram if all angles are right angles.

___ 29.  If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, the

___ 30.  Two parallel lines determine a plane.

___ 31.  If a plane contains one of two skew lines, it contains the other.

___ 32.  If a line and a plane never meet, they are parallel.

___ 33.  If two parallel lines lie in different planes, the planes are parallel.

___ 34.  If a line is perpendicular to two planes, the planes are parallel.

___ 35.  If a plane and a line not in the plane are each perpendicular to the same line, then they are

parallel to each other.

___ 36.  In a plane, two lines perpendicular to the same line are parallel.

___ 37.  In space, two lines perpendicular to the same line are parallel.

___ 38.  If a line is perpendicular to a plane, it is perpendicular to every line in the plane.

___ 39.  If a line is perpendicular to a line in a plane, it is perpendicular to the plane.

___ 40.  Two lines perpendicular to the same line are parallel.

___ 41.  Three parallel lines are coplanar.