Geometry Quiz: Formal Geometric Constructions

What this quiz covers

This quiz focuses on Formal Geometric Constructions, giving you a quick way to practice the rules, question types, and explanations that matter most for Geometry.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $WXYZ$ must be a rectangle since its diagonals are congruent and bisect each other (correct answer)
2. $WXYZ$ must be a parallelogram since its diagonals bisect each other completely
3. $WXYZ$ must be a rhombus since its diagonals are congruent and bisect each other
4. $WXYZ$ could be any quadrilateral since diagonal properties don't determine the shape

Question 2

1. It is a line through $A$ parallel to $\overline{AB}$.
2. It is a line through points equidistant from $A$ and $B$. (correct answer)
3. It is the segment $\overline{AB}$ extended beyond $B$.
4. It is a line that must pass through point $A$.

Question 3

1. Different widths can make the intersection point not equidistant from $D$ and $E$. (correct answer)
2. Different widths guarantee the bisector is still correct by symmetry of the picture.
3. Different widths force $\angle ABC$ to become a right angle.
4. Different widths are allowed because only straight lines matter in the end.

Question 4

1. Draw arcs centered at $A$ and $B$ with the same compass width.
2. Mark the intersection points of the arcs as $P$ and $Q$.
3. Draw the line through $P$ and $Q$.
4. Measure $\overline{AB}$ to confirm the midpoint location before drawing $\overleftrightarrow{PQ}$. (correct answer)

Question 5

1. Line $PQ$ contains all points equidistant from $A$ and $B$. (correct answer)
2. Line $PQ$ contains all points equidistant from $P$ and $Q$.
3. Line $PQ$ contains all points closer to $A$ than to $B$.
4. Line $PQ$ contains all points that make $\angle APB$ a right angle.

Question 6

1. If a transversal creates congruent corresponding angles, then the two lines are parallel. (correct answer)
2. The copied angle is correct because the diagram is drawn to scale.
3. The new line is parallel because it is the same distance from $\ell$ everywhere.
4. Parallel lines can be constructed only by drawing two perpendiculars.

Question 7

1. Points $P$ and $Q$ are each equidistant from $A$ and $B$, so line $PQ$ is the perpendicular bisector of $\overline{AB}$. (correct answer)
2. Line $PQ$ is a perpendicular bisector because it visually crosses $\overline{AB}$ in the middle.
3. Line $PQ$ must be perpendicular because the circles are drawn with large radii.
4. The midpoint is found by measuring $\overline{AB}$ and marking half of it.

Question 8

1. $m$ is parallel to $\ell$ because corresponding angles formed by the transversal are congruent. (correct answer)
2. $m$ is perpendicular to $\ell$ because the copied angle must be a right angle.
3. $m$ is parallel to the transversal because it shares point $P$ with the transversal.
4. $m$ is parallel to $\ell$ because the arcs are symmetric about point $P$ in the drawing.

Question 9

1. Point $F$ (the arc intersection) is guaranteed to be equidistant from $D$ and $E$.
2. Ray $\overrightarrow{BF}$ is guaranteed to bisect $\angle ABC$.
3. The construction does not guarantee that $\overrightarrow{BF}$ bisects the angle. (correct answer)
4. The construction guarantees $\overrightarrow{BF}\perp \overleftrightarrow{DE}$.

Question 10

1. $11$ (correct answer)
2. $5$
3. $22$
4. $10$

Question 11

1. $\angle JLK = 28°$
2. $\angle JLK = 35°$ (correct answer)
3. $\angle JLK = 117°$
4. $\angle JLK = 145°$

Question 12

1. $QT = 6$
2. $QT = 8$ (correct answer)
3. $QT = 10$
4. $QT = 12$

Question 13

1. The theorem that states if one pair of opposite sides is both parallel and congruent, then the quadrilateral is a parallelogram
2. The theorem that states if both pairs of opposite sides are congruent, then the quadrilateral is a parallelogram
3. The theorem that states if the diagonals bisect each other, then the quadrilateral is a parallelogram (correct answer)
4. The theorem that states if one pair of opposite angles is congruent, then the quadrilateral is a parallelogram

Question 14

1. $BD = 11$
2. $BD = 19$
3. $BD = 22$ (correct answer)
4. $BD = 38$