Formal Geometry Semester 1 Instructional Materialspowersrhs.weebly.com/uploads/2/0/7/0/20701342/... · Formal Geometry Semester 1 Instructional Materials 2013-2014 Revised 11-18-13

Formal Geometry Semester 1 Instructional Materials 2013-2014

Revised 11-18-13

2013-2014

Formal Geometry Semester 1

Instructional Materials for the WCSD Math Common Finals

The Instructional Materials are for student and teacher use and are aligned

to the Math Common Final blueprint for this course. When used as test

practice, success on the Instructional Materials does not guarantee success

on the district math common final.

Students can use these Instructional Materials to become familiar with the

format and language used on the district common finals. Familiarity with

standards vocabulary and interaction with the types of problems included

in the Instructional Materials can result in less anxiety on the part of the

students.

Teachers can use the Instructional Materials in conjunction with the course

guides to ensure that instruction and content is aligned with what will be

assessed. The Instructional Materials are not representative of the depth

or full range of learning that should occur in the classroom


Revised 11-18-13

Multiple Choice: Identify the choice that best completes the statement or answers the question. Figures are not necessarily drawn to scale.

1. Using slope and/or distance formulas, identify which of the following is the best name for

the figure: ( ) ( ) ( ).

A. scalene triangle

B. isosceles triangle

C. equilateral triangle

D. obtuse triangle

2. ( ) is the midpoint of . The coordinates of are ( ). What are the coordinates

of R?

A. ( )

B. ( )

C. ( )

D. ( )

3. Given the following:

is a complement of

is a supplement of

is a supplement of

is a complement of

is a complement of

is a supplement of

Then

A. C.

B. D.

4. For a coordinate proof concerning an isosceles triangle, which coordinates might be easiest

to use?

A. ( ) ( ) ( ) C. ( ) ( ) ( )

B. ( ) ( ) ( ) D. ( ) ( ) ( )


Revised 11-18-13

5. In the figure, which pair of angles is supplementary?

A.

1 2

34

5 6

78

B.

C.

D.

6. Which of the following are logically equivalent?

A. A statement and its converse

B. A statement and its inverse

C. A statement and its contrapositive

D. A statement, its converse, its inverse and its contrapositive

7. Two lines that do NOT intersect are always parallel.

Which of the following best describes a counterexample to the assertion above?

A. coplanar lines

B. parallel lines

C. perpendicular lines

D. skew lines

8. Determine which statement follows logically from the given statements.

If I am absent on a test day, I will need to make up the test. Absent students take the test

during their lunch time or after school.

A. If I am absent, it is because I am sick.

B. If I am absent, I will take the test at lunch time or after school.

C. Some absent students take the test at lunch time.

D. If I am not absent, the test will not be taken at lunch time or after school.


Revised 11-18-13

9. Determine whether the conjecture is true or false. Give a counterexample for any false

conjecture.

Given: Two angles are supplementary.

Conjecture: They are both acute angles.

A. False; either both are right or they are adjacent.

B. True

C. False; either both are right or one is obtuse.

D. False; they must be vertical angles.

10. Write the statement in if-then form.

A counterexample invalidates a statement.

A. If it invalidates the statement, then there is a counterexample.

B. If there is a counterexample, then it invalidates the statement.

C. If it is true, then there is a counterexample.

D. If there is a counterexample, then it is true.

11. Which statement is true based on the figure?

A.

65

65

60

60

110

110

120

120 e

d

c

b

a

B.

C.

D.


Revised 11-18-13

For #12-13 use the following:

Given: bisects

Prove:

3 2

1K

L

M

J

Statements Reasons

bisects Given

12.

13.

Substitution Property of Equality

12. Choose one of the following to complete the proof.

A. Definition of angle bisector- If a ray is an angle bisector, then it divides the angle into

two congruent angles.

B. Definition of opposite rays- If a point on the line determines two rays are collinear,

then the rays are opposite rays.

C. Definition of ray- If a line begins at an endpoint and extends infinitely, then it is ray.

D. Definition of segment bisector- If any segment, line, or plane intersects a segment at its

midpoint then it is the segment bisector.


A. Definition of complementary angles- If the angle measures add up to , then angles

are supplementary

B. Supplemental Angle Theorem- If two angles are supplementary to a third angle then

the two angles are congruent

C. Definition of supplementary angles- If the angles are supplementary, then the angle’s

measures add to .

D. Vertical Angle Theorem- If two angles are vertical angles, then they have equal

measures.


Revised 11-18-13

14. Complete the statement:

If two lines are perpendicular, then ___________________________________________.

A. the lines do not intersect

B. the slopes of the two lines are equal

C. the product of the slopes for the two lines is equal to negative one

D. the product of the slopes for the two lines is equal to zero

15. The equations of four lines are given. Identify which lines are parallel.

I.

II.

III.

( )

IV.

A. I, II, and IV C. III and IV

B. I and II D. None of the lines are parallel

16. Which equation of the line passes through ( ) and is perpendicular to the graph of the

line that passes through the points( ) and ( )?

A. C.

B.

D.

17. Which equation of the line passes through ( ) and is perpendicular to the graph of the

line

?

A.

C.

B.

D.


Revised 11-18-13


Given:

Prove:

1 2

34

5 6

78

p

q

t

Statements Reasons

Given

14. Alternate Interior Angles Theorem

15.

Substitution Property of Equality


A.

B.

C.

D.


A. Vertical Angle Theorem- If two angles are vertical angles, then they have equal angle

measures

B. Congruent Supplements Theorem- If two angles are supplementary to a third angle

then they are congruent

C. Linear Pair Theorem- If two angles form a linear pair, then the angles are

supplementary and their angle measures add to

D. Definition of complementary angles- If two angles are a linear pair, then the angles are

complementary and their angle measures add to


Revised 11-18-13

20. Line k is represented by the equation, . Which equation would you use to

determine the distance between the line k and point ( )?

A. C.

B.

D.

21. Which of the following terms best describe the transformation below?

A. dilation

B. reflection

C. rotation

D. translation

22. Which of the following is true?

A. All triangles are congruent.

B. All congruent figures have three sides.

C. If two figures are congruent, there must be some sequence of rigid transformations that

maps one to the other.

D. If two triangles are congruent, then they must be right angles.

23. Point Y of is ( ). What is the image of Y after is transformed using the

translation ( )?

A. ( ) C. ( )

B. ( ) D. ( )


Revised 11-18-13

24. What are the coordinates for the image of after a rotation clockwise about the

origin and a translation of ( ) ( )?

A. ( ) ( ) ( )

B. ( ) ( ) ( )

C. ( ) ( ) ( )

D. ( ) ( ) ( )

25. The point ( ) is rotated counterclockwise about the origin, and then the image

is reflected across the line . What are the coordinates of the final image ?

A. ( ) C. ( )

B. ( ) D. ( )

26. Point A is reflected over the line . Which of the following is NOT true of line ?

A. line is perpendicular to line

B. line is perpendicular to line

C. line bisects line segment

D. line bisects line segment

27. What is the scale factor for the dilation of

to image ?

A.

B.

C.

D.

G

K

H


Revised 11-18-13

28. Apply the dilation ( ) ( ) to the triangle given below. Which of the

following is the perimeter of the image?

A.

B.

C.

D.

29. If , which of the following is true?

A.

B.

C.

D.

30. In the figure and . What information is needed to prove that

by SAS?

A.

A

G

E

L

D

O

B.

C.

D.

31. In the figure and . Which of the following statements is about

congruence is true?

A. by ASA

B. by SSS

C. by SAS

D. by SAS


Revised 11-18-13

32. Refer To the figure to complete the congruence statement, .

A.

B.

C.

D.

33. Which theorem can be used to conclude that ?

A. SAA

B

A

C

E

D

B. SAS

C. SSS

D. AAA

34. In The figure and . Which theorem can be used to conclude that

?

A. SSA

B. AAA

C. SAS

D. HL

35. In the figure, . What is the ?

A.

B.

C.

D.


Revised 11-18-13

37. Determine which postulate or theorem can be used to prove the pair of triangles congruent.

A. AAS

B. SAS

C. ASA

D. SSS

36. Given , Anna is proving . Which statement should be part of

her proof?

A.

M

N

P

1

2

3 4

B.

C.

D.


Revised 11-18-13

For #38 use the following:

Given: is the midpoint of ;

Prove:

Statements Reasons

is the midpoint of ; Given

[1] Definition of Midpoint

Given

Reflexive property of congruence

[2]


A. [1]

[2] SAS Congruence

B. [1]

[2] SAS Congruence

C. [1]

[2] Linear Pair Theorem

D. [1]

[2] AAS Congruence

39. In the figure, . What is the value of y?

A.

B.

C.

D.


Revised 11-18-13

40. In a coordinate proof, which of the following would be most useful to prove that triangles

are congruent by the SSS Triangle Congruence Theorem?

A. Distance formula

B. Midpoint formula

C. Corresponding parts of congruent triangles are congruent (CPCTC)

D. Slope formula

41. In the figure, . Find

the in terms of x.

C

A

E

B

A.

B.

C.

D.


Revised 11-18-13

For #42 use the following:

Given: and

Prove:

Statements Reasons

Given

39.

Given

Transitive property of congruence

Corresponding Angles Theorem


A. Isosceles Triangle Symmetry Theorem- If the line contains the bisector of the vertex

angle of an isosceles triangle, then it is a symmetry line for the triangle.

B. Isosceles Triangle Coincidence Theorem- If the bisector of the vertex angle of an

isosceles triangle is also the perpendicular bisector of the base, then the median to the

base is the same line

C. Isosceles Triangle Base Angle Converse Theorem- If two angles of a triangle are

congruent, the sides opposite those angles are congruent

D. Isosceles Triangle Base Angle Theorem- If two sides of a triangle are congruent, then

the angles opposite those sides are congruent

43. Suppose you wish to prove the following using indirect proof.

If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Which of the following would you try to contradict in an indirect proof.

A. Two parallel lines are cut by a transversal.

B. Alternate interior angles are congruent.

C. Alternate interior angles are not congruent.

D. Two parallel lines are not cut by a transversal.


Revised 11-18-13

44. Which of the following best describes the shortest distance from a vertex of a triangle to the

opposite side?

A. altitude

B. diameter

C. median

D. segment

45. is the angle bisector of . What is the value of x?

A.

B.

C.

D.


Revised 11-18-13


Given: is a median of isosceles Prove:

Statements Reasons

is a median Given

41.

42. Definition of isosceles triangle

Reflexive property of congruence

SSS Congruence


A. Definition of angle bisector- If a ray divides an angle into two congruent angles, then it

is an angle bisector.

B. Definition of segment bisector- If any segment, line, or plane intersects a segment at its

midpoint, then it is a segment bisector.

C. Definition of isosceles triangle- If a triangle has at least two congruent sides, then it is

an isosceles triangle.

D. Definition of median- If a segment is a median, then it has endpoints at the vertex of a

triangle and the midpoint of the opposite side.


A.

B.

C.

D.


Revised 11-18-13

48. Reflect point H across the line to form point H’, which of the following is true?

A. H

F

G

B.

C.

D.

49. Given the diagram, what kind of line is ?

A. altitude

B. median

C. angle bisector

D. perpendicular bisector

50. Find the range of values containing x.

A.

B.

C.

D.

Documents

Formal Geometry Semester 1 Instructional Materialspowersrhs.weebly.com/uploads/2/0/7/0/20701342/... · Formal Geometry Semester 1 Instructional Materials 2013-2014 Revised 11-18-13