1.

Fill in a reason to complete this proof.

If , then .

Statement

Reason

Given

Vocabulary Bank:

Multiplication Property of Equality

Distributive Property

Substitution Property of Equality

Subtraction Property of Equality

Symmetric Property of Equality

2.

Which description best defines ?

a)The set of all points between point F and point G

b)The set of all points between point F and point G, including point F and point G

c)The set of all points that are the same distance from point F as point G

d)The set containing point F and point G

3.

Fill in each of the blanks using the word back to correctly complete the statement.

A reflection is a transformation that maps point A in a figure over a line, , such that for point P at the intersection of and _________________________ and __________________________.

Word bank

Point P is the midpoint of

Point P is the midpoint of

4.

Which figures demonstrate a single rotation?

a)

b)

c)

d)

5.

What is the smallest degree of rotation that will map a regular 18-gon onto itself?

6.

What is the sequence of tranformations that Maps ABC to A'B'C'?

Step 1: _______________________

Step 2: _______________________

7.

The coordinates of the vertices of trapezoid EFGH are E(-8, 8), F(-4, 12), G(-4, 0), and H(-8, 4).The coordinates of the vertices of trapezoid E'F'G'H' are E'(-8, 6), F'(-5, 9), G'(5, 0), and H'(-8, 3).

Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E'F'G'H'?

a)Trapezoid EFGH is congruent to trapezoid E'F'G'H' because you can map trapezoid EFGH to trapezoid E'F'G'H' by reflecting it across the x-axis and then translating it up 14 units, which is a sequence of rigid motions.

b)Trapezoid EFGH is congruent to trapezoid E'F'G'H' because you can map trapezoid EFGH to trapezoid E'F'G'H' by translating it down 2 units and then reflecting it over the y-axis, which is a sequence of rigid motions

c)Trapezoid EFGH is congruent to trapezoid E'F'G'H' because you can map trapezoid EFGH to trapezoid E'F'G'H' by dilating it by a factor of 34 and then translating it 2 units left, which is a sequence of rigid motions

d)Trapezoid EFGH is not congruent to trapezoid E'F'G'H' because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E'F'G'H'.

8.

Which statement explains why ?

A.You can map onto by rotating it about the origin and translating it 2 units right, which is a sequence of rigid motions.

B.You can map onto by reflecting it across the y-axis and translating it 6 units down, which is a sequence of rigid motions

C.You can map onto by rotating it clockwise about the origin and translating it 4 units left, which is a sequence of rigid motions

D.You can map onto by reflecting it across the x-axis and translating it 6 units left, which is a sequence of rigid motions.

9.

Which postulate or theorem proves ?

A.

SSS Congruence Postulate

B.SAS Congruence Postulate

C.HL Congruence Theorem

D.ASA Congruence Postulate

10.

Complete the Proof

Statement

Reason

Given

Draw median

Two points determine a line

Point M is the midpoint of

Definition of midpoint

Reflexive Property of Congruence

Bank:

CPCTC

Definition of median

SSS Congruence Postulate

HL Congruence Theorem

11.

Complete the proof

Statement

Reason

Parallelogram EFGH

Given

ASA Congruence Postulate

CPCTC

bisects and bisects

Definition of Bisector

Word bank:

Definition of a parallelogram

The opposite sides of parallelograms are congruent

When two parallel lines are cut by a transversal, alternate interior angles are congruent

When two parallel lines are cut by a transversal, corresponding angles are congruent

12.

Complete the proof

Statement

Reason

Parallelogram MNPQ

Given

The opposite sides of a parallelogram are congruent

Reflexive Property of Congruence

Bank:

CPCTC

&

SAS Congruence Postulate

SSS Congruence Postulate

Vertical angles are congruent

13.

Complete the proof

It is given that is a rectangle.By the _____________________, and are right angles, and because all right angles are congruent, .because ___________________, and by the ________________________.By the ___________________ .Because corresponding parts of congruent triangles are congruent,

Bank:

Definition of a parallelogram

Definition of a rectangle

Reflexive property of congruence

Transitive property of congruence

Opposite sides of a rectangle are congruent

Midpoints divide segments into congruent parts

SAS congruence postulate

SSS congruence postualte

HL congruence theorem

14.

15.

What are the coordinates of the midpoing of the segment whose endpoints are and ?