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

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 3

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 4

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 5

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 6

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 7

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 8

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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