Question 1

In the diagram below, $\overline{AEFB} \parallel \overline{CGD}$, and $\overline{GE}$ and $\overline{GF}$ are drawn.

If $m\angle EFG=32 \degree$, what is $m\angle EGF$?

Accepted Answer

$105\degree$

Answer

$75\degree$

Answer

$43\degree$

Answer

$11\degree$

Question 2

If $\Delta ABC$ is mapped onto $\Delta DEF$ after a line reflection and  $\Delta DEF$ is mapped onto  $\Delta XYZ$ after a translation, the relationship between  $\Delta ABC$  and  $\Delta XYZ$ is that they are always

Accepted Answer

congruent and similar

Answer

neither similar nor congruent

Answer

similar but not congruent

Answer

congruent but not similar

Question 3

In regular hexagon $ABCDEF$ shown below,  $\overline {AD}$,  $\overline {BE}$, and  $\overline {CF}$ all intersect at  $G$.

When  $\Delta ABG$ is reflected over $\overline {BG}$  and then rotated $180 \degree$ about point $G$,  $\Delta ABG$ is mapped onto

Accepted Answer

$\Delta FEG$

Answer

$\Delta CBG$

Answer

$\Delta AFG$

Answer

$\Delta DEG$

Question 4

In the diagram below, $\overline{AKS}$, $\overline{NKC}$, $\overline{AN}$, and $\overline{SC}$, are drawn such that $\overline{AN} \cong \overline{SC}$.

Which additional statement is sufficient to prove $\Delta \overline{KAN} \cong \Delta \overline{KSC}$ by $AAS?$

Accepted Answer

$\overline {AN} \parallel \overline {SC}$

Answer

$\overline{AS}$ and $\overline{NC}$ bisect each other.

Answer

$K$ is the midpoint of  $\overline {NC}$.

Answer

$\overline {AS} \bot \overline {CN}$

Question 5

Quadrilateral $MATH$ has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral $MATH$ is always true?

Accepted Answer

$\angle{MAT} \cong\angle{MHT}$

Answer

$\overline{MT} \bot\overline{AH}$

Answer

$\overline{MT} \cong \overline{AH}$

Answer

$\angle{MHT} \cong\angle{ATH}$

Question 6

In the diagram below, rectangle $ABCD$ has vertices whose coordinates are $A(7,1), B(9,3), C(3,9),$ and $D(1,7).$

Which transformation will not carry the rectangle onto itself?

Accepted Answer

a rotation of $180 \degree$ about the point $(6, 6)$

Answer

a rotation of $180 \degree$ about the point $(5, 5)$

Answer

a reflection over the line $y= x$

Answer

a reflection over the line $y=- x+10$

Question 7

In $\Delta ABC, \overline{BD}$ is the perpendicular bisector of $\overline {ADC}$. Based upon this information, which statements below can be proven?

I. $\overline{BD}$ is a median.
II. $\overline{BD}$ bisects $\angle {ABC}$.
III. $\Delta ABC$ is isosceles.

Accepted Answer

I, II, and III

Answer

I and II, only

Answer

II and III, only

Answer

I and III, only

Question 8

In the diagram below $\Delta ABC$ with sides of 13, 15, and 16, is mapped onto $\Delta DEF$ after a clockwise rotation of $90\degree$  about point $P$.

If $DE =2x -1$, what is the value of $x$?

Accepted Answer

8.5

Answer

7.5

Answer

8

Answer

7

Question 9

The figure below shows a rhombus with noncongruent diagonals.
Which transformation would $not$ carry this rhombus onto itself?

Accepted Answer

a clockwise rotation of $90\degree$ about the intersection of the diagonals

Answer

a reflection over the longer diagonal

Answer

a reflection over the shorter diagonal

Answer

a counterclockwise rotation of $180\degree$ about the intersection of the diagonals

Question 10

In rhombus $VENU$, diagonals $\overline {VN}$ and $\overline {EU}$ intersect at $S$. If $VN=12$  and $EU=16$, what is the perimeter of the rhombus?

Accepted Answer

40

Answer

80

Answer

10

Answer

20

Question 11

Which statement about parallelograms is always true?

Accepted Answer

The diagonals bisect each other.

Answer

The diagonals are perpendicular.

Answer

The diagonals are congruent.

Answer

The diagonals bisect their respective angles.

Question 12

In the diagram below of triangle  $ABC, \overline {AC}$ is extended through point $C$ to point $D$, and $\overline{BE}$ is drawn to $\overline {AC}$.

Which equation is always true?

Accepted Answer

$m\angle7=m \angle3+m \angle2$

Answer

$m\angle6=m \angle3- m \angle2$

Answer

$m\angle1=m \angle3+ m \angle2$

Answer

$m\angle5=m \angle3- m \angle2$

Question 13

In the diagram of quadrilateral $NAVY$ below, $m\angle YNA=30\degree, m\angle YAN=38\degree, m\angle AVY=94\degree,$ and $m\angle VAY=46\degree$.

Which segment has the shortest length?

Accepted Answer

$\overline {VA}$

Answer

$\overline {NY}$

Answer

$\overline {AY}$

Answer

$\overline {VY}$

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