Regular Geometry 1st Semester Review Packet

1) Explain what it means to bisect a segment. Why is it impossible to

bisect a line?

2) Are all linear pairs supplementary angles? Are all supplementary angles

linear pairs? Explain.

3) Explain why a four-legged table may rock from side to side even if the

floor is level. Would a three-legged table on the same level floor rock

from side to side? Why or why not?

4) Can two planes intersect in a segment? Explain.

Short Answer: Answer each question completely.

5) Sketch the figure described.

Three lines that lie in a plane and intersect at one point

6)

Use the figure to the right to answer the

following questions.

a) Name the intersection of plane CDF and

plane BAD.

b) Are the points B and F collinear?

c) Are the points B and F coplanar?

d) Name three planes that intersect at

point A.

7) Point S is between R and T on RT . Use the given information to write

an equation in terms of x. Solve the equation. Then find RS and ST.

RS = 2x + 10

ST = x – 4

RT = 21

8) Point M is the midpoint of RT . Find RM, MT, and RT.

9) The endpoints of two segments are given. Find the length of the

segment rounded to the nearest tenth. Then find the coordinate of

the midpoint of the segment.

A(2, 5) and B(4, 3)

10) Point C(3, 8) is the midpoint of AB . One endpoint is A(-1, 5). Find the

coordinates of endpoint B.

11) Find ABCm and CBDm if ABDm = 120.

12) VZ bisects UVW , and oUVZm 81 . Find .UVWm Then classify

UVW by its angle measure.

13) If 2m = 6x - 1 and the 4m = 4x + 17, then find the 3m .

14) 21 and are complementary angles. Find the measures of the angles

when oxm )10(1 and oxm )402(2 .

15) Pentagon ABCDE is a regular polygon. The length of BC is represented

by the expression 5x – 4. The length of DE is represented by the

expression 2x + 11. Find the length of AB .

16) Draw a sketch of a concave pentagon.

17) Draw an example of a linear pair.

Fill-in the blank: Fill in the blank with the most appropriate word.

18) A ___________ has a definite beginning and end.

19) A ____________ has a definite starting point and extends without

end in one direction.

20) ___________ are two rays that are part of the same line and

have only their endpoints in common.

21) You can use a _________ to measure angles and sketch angles of

given measure.

22) Angles with the same measure are ____________________.

23) Two angles are __________________ if and only if (iff) the

sum of their degree measure is 180.

24) A regular polygon is both ___________ and ___________.

25) Describe the pattern in the numbers. Write the next three

numbers.

-6, -1, 4, 9, …

26) Write the if-then form, the converse, the inverse, and the

contrapositive for the given statement.

All right angles are congruent.

If-then:

Converse:

Inverse:

Contrapositive:

27) If you decide to go to the football game, then you will miss band

practice. Tonight, you are going to the football game. Using the Law of

Detachment, what statement can you make?

2

28) If you get an A or better on your math test, then you can go to

the movies. If you go to the movies, then you can watch your favorite

actor. Using the Law of Syllogism, what statement can you make?

29) Show that the conjecture is false by finding a counterexample.

The sum of two numbers is always greater than the larger number.

Use the diagram to write examples of the stated

postulate.

30) A line contains at least two points

31) A plane contains at least three noncollinear points.

32) If two planes intersect, then their

intersection is a line.

33) Sketch a diagram that represents the given

information: straight angle CDE is bisected by DK .

Solve the equation. Write a reason for each step.

34) -7(-x + 2) = 42

Name the property illustrated by the statement.

35) If DEFJKLJKLDEF then ,

36) CC 37) If om 574 , find .3and,2,1 mmm

38) Find the measure of each angle in the diagram.

1 4

3

7y - 12

4

x 6y + 8

6x - 26

39) How can you show that the statement, “If you play a sport, then

you wear a helmet.” Is false? Explain.

40) Use deductive reasoning to make a statement about the picture.

41) What is a theorem? How is it different from a postulate?

42) Explain why writing a proof is an example of deductive

reasoning, not inductive reasoning.

43) Describe the relationship between the angle measures of

complementary angles, supplementary angles, vertical angles, and

linear pairs.

44) Complete one of the following proofs.

a) Given : AC = AB + AB

Prove: AB = BC

Statements Reasons

1. AC = AB + AB 1. Given

2. AB + BC = AC 2.

3. AB + AB = AB + BC 3. Transitive Property of Equality

4. AB = BC 4.

B

b) Given: AB is a line segment

Prove: AB AB Statements Reasons

1. AB is a line segment 1. Given

2. AB is the length of AB 2. Ruler Postulate

3. AB = AB 3.

4. AB AB 4.

c) Given: ,A B B C

Prove: A C Statements Reasons

1. ,A B B C 1. Given

2. ,m A m B m B m C 2.

3. m A m C 3. Transitive Property of Eq

4. A C 4.

1) Complete the statement.

a. 4 and _____are corresponding angles.

b. 3 and _____are consecutive interior angles.

c. 5 and _____ are alternate interior angles.

d. 7 and _____are alternate exterior angles.

2) Find the value of x. Explain your reasoning.

3) Find the value of x. Explain your reasoning.

4) Find the value of x. Explain your reasoning.

Find the value of x that makes m n .

5)

6)

7)

8) A line that intersects two other lines is a _____________________.

9) Find the values of x and y.

10) Draw a pair of parallel lines with a transversal. Identify all pairs of

alternate exterior angles.

11) What angle pairs are formed by transversals?

12) Michaela was stenciling this design on her bedroom walls. How can she

tell if the top and bottom lines of the design are parallel?

13) In the figure each rung of the ladder is parallel to the rung directly

above it. Explain why the top rung is parallel to the bottom rung.

14) How do you find the slope of a line given the coordinates of two points

on the line?

15) Find the slope of the line that passes through the points

(3, 5) and (5, 6).

Tell whether lines through the given points are parallel, perpendicular,

or neither. Justify your answer.

16) Line 1: (1, 0), (7, 4)

Line 2: (7, 0), (3, 6)

17) Line 1: (-3, 1), (-7, -2)

Line 2: (2, -1), (8, 4)

18) Graph the line through the given point with the given slope.

P(3, -2), slope: -3

19) Write an equation of the line in slope-intercept form passing through

the point (2, -3) that is parallel to the line with the equation

y = 6x + 4.

20) Write an equation of the line in slope-intercept form passing

through the point (3, -4) that is perpendicular to the line with the

equation 1

12

y x .

21) What does intercept means in the expression slope-intercept form?

Use complete sentences.

22) Explain how you can use the standard form of a linear equation

to find the intercepts of a line. Use complete sentences.

23) Draw a line with an undefined slope on the coordinate plane.

24) The ______________________ segment is the shortest

distance between a point and a line.

25) In the diagram, AB BC . Find the value of x.

26) Can a right triangle also be obtuse? Explain why or why not.

27) What must be true of a transformation for it to be a rigid

motion?

28) List three examples for transformations that are rigid motions.

29) How can you use side lengths to prove triangles congruent?

30) A triangle with three congruent angles is called ___________.

31) Describe the difference between isosceles and scalene triangles.

32) Draw right isosceles triangle.

33) Draw an acute scalene triangle.

Find the value of x. Then classify the triangle by its angles.

34)

35)

36)

37)

38) Find the measure of angle 1.

39) Find mJKM.

40) Write all the congruence statements for the figures.

1

41) Identify the transformation you could use to move the solid figure onto

the dashed figure.

42) Find the values of x and y. ABCD EFGH

43) Explain why the bench with the diagonal support is stable, while the one

without support can collapse.

44) Explain how you could show that the triangles are congruent in the

figure.

45) Explain the difference between proving triangles congruent

using the ASA and AAS Congruence Postulates.

46) You know that a pair of triangles has two pairs of congruent

corresponding angles. What other information do you need to show

that the triangles are congruent?

47) Explain what CPCTC is and why is it useful?

48) The angle between two sides of a triangle is called the

_________________ angle.

49) Are isosceles triangles always acute triangles? Explain your

reasoning.

Use the given information to name two triangles that are congruent, if

possible. Explain your reasoning by stating the postulate and the

congruence statements for the sides and/or angles that you used.

50) RSTUV is a regular pentagon.

51)

52)

53)

V

U

T

S

R

Q

D A

U

D C

B

A

S

T

R

A

P

54)

55)

State the third congruence that must be given to prove that

DEFABC using the indicated postulate.

Given: __________,, FECBDEAB

Use the SSS Congruence Postulate.

Given: __________,, FDCADA

Use the SAS Congruence Postulate.

Given: __________,, EBEFBC

Use the ASA Congruence Postulate.

Find the values of x and y.

56)

57)

H

T A

M

F

E

D

C

B

A

D

U

M

5 5

5

3xo

yo

55o

(x+7)o

yo

58) Find the values of angles 1, 2, 3, and 4.

59) Choose two proofs to complete by filling in

the blanks. You may choose to do more than the required two for

extra credit.

a) Prove that TURRST .

Statements Reasons

1. ________________ Given

2. RT TR ______________

3. TURRST ______________

b) Prove that ABD CBD .

Statements Reasons

1._______________ Given

2. ADB CDB All right angles

are congruent

3. _____________ reflexive prop

of congruence

4. ABD CBD _______

R

T

U

S

D C

B

A

c) Given: UGBU ; BGtsbiUM sec

Prove: MUGBUM

Statements Reasons

1. UGBU , BGtsbiUM sec given

2. BM GM Definition of a bisector

3. __________________ reflexive property of congruence

4. BUM MUG _________________

5. MUGBUM _________________

d) Given: B is the midpoint of CD ; 21

Prove: EA

Statements Reasons

1. B is the midpoint of CD ; 21 given

2. BC BD definition of midpoint

3. CBA DBE _____________________

4. CBA DBE _____________________

5. EA _____________________

U

M G B

2

E

D

C

A

B

1

WY is the midsegment of ΔQRS. Find the value of x.

1) 2)

3)

Find the value of x.

4)

5)

In the diagram, the perpendicular bisectors of ΔWXY meet at point Z.

Find the indicated measure.

6) WZ 7) ZY

Find the coordinates of the centroid P of ΔSTU.

8) S(2, 5), T(5, –2), U(–1, –6)

9) S(–1, 7), T(5, –6), U(–7, –4)

In ΔABC, Q is the centroid. Find the indicated length. Show your work.

10) QC = 12. Find QM. 11) QC = 6. Find CL.

List the sides and the angles in order from smallest to largest.

12)

13)

Is it possible to construct a triangle with the given side lengths? Justify

your answer.

14)10, 7, 13

15)26, 20, 2

Describe the possible lengths of the third side of the triangle

given the lengths of the other two sides.

16) 5 inches, 6 inches

17) 14 feet, 21 feet

Complete the statement with <, >, or =.

18) AB_____ BC 19) RS _____ VU

20) Suppose you wanted to prove the statement “If x + y > 20 and y = 5,

then x > 15.” What temporary assumption could you make to

prove the conclusion indirectly?

Use the Hinge Theorem or its converse and properties of triangles to

write and solve an inequality to describe a restriction on the value of x.

21) 22)