Quick Review Flashcards - Click to flip and test your knowledge!
Question
What should always be drawn before starting the actual construction of a quadrilateral?
Answer
A rough free-hand sketch.
Question
To 'construct' a quadrilateral essentially means to find or locate its four _____.
Answer
vertices
Question
When constructing a quadrilateral with four sides and one angle given, what is the first line segment to be drawn?
Answer
The base side adjacent to the given angle.
Question
If quadrilateral $ABCD$ has $AB = 3.5\text{ cm}$, $BC = 4.0\text{ cm}$, and $\angle B = 45^{\circ}$, which point is located by cutting an arc of $3.5\text{ cm}$ from point $B$?
Answer
Vertex $A$
Question
When constructing a quadrilateral with three sides and two consecutive angles, which side is typically drawn first?
Answer
The side included between the two given angles.
Question
In the construction of a quadrilateral with four sides and one diagonal, the first step is to construct a _____ using three of the given dimensions.
Answer
triangle
Question
If quadrilateral $ABCD$ has sides $AB$, $BC$, $CD$, $DA$ and diagonal $AC$ given, which vertex is found by the intersection of arcs from $A$ and $C$ after $\Delta ABC$ is built?
Answer
Vertex $D$
Question
What is the first procedural step to construct a quadrilateral when three sides and two diagonals are known?
Answer
Construct a triangle using one side and both diagonals (or two sides and one diagonal).
Question
In a parallelogram, what is the relationship between opposite sides regarding their length?
Answer
Opposite sides are equal.
Question
If parallelogram $ABCD$ has $AB = 3.0\text{ cm}$ and $BC = 4.0\text{ cm}$, what is the length of side $AD$?
Answer
$4.0\text{ cm}$
Question
To construct a parallelogram when two consecutive sides and the included angle are given, one first constructs a _____.
Answer
triangle
Question
What key geometric property of parallelogram diagonals is used for construction when only one side and both diagonals are given?
Answer
The diagonals bisect each other.
Question
In a parallelogram with diagonals $AC$ and $BD$ intersecting at $O$, if $BD = 5.0\text{ cm}$, what is the length of segment $OB$?
Answer
$2.5\text{ cm}$
Question
When constructing a parallelogram from its diagonals, what is the purpose of 'producing' segment $BO$ to $D$ such that $OD = OB$?
Answer
To locate the fourth vertex while ensuring the diagonals bisect each other.
Question
If a parallelogram must be constructed with two diagonals and an included angle, what is the first step?
Answer
Draw one diagonal and locate its mid-point $O$.
Question
Why might you start a parallelogram construction with diagonal $BD = 4.5\text{ cm}$ instead of $AC = 5.4\text{ cm}$ if the included angle is given?
Answer
If half of the other diagonal ($2.25\text{ cm}$) cannot be accurately measured on a standard scale.
Question
In the construction of a parallelogram using height, what is drawn through the height point $E$ to be parallel to the base $BC$?
Answer
A perpendicular line to the altitude $CP$.
Question
To construct a trapezium $ABCD$ where $AD \parallel BC$, what is the first segment usually drawn?
Answer
The base $BC$.
Question
In a trapezium construction with four sides given, why is a point $E$ marked on $BC$ such that $BE = AD$?
Answer
To create a triangle $DEC$ where $DE$ is equal to side $AB$.
Question
What is the measure of every interior angle in a rectangle?
Answer
$90^{\circ}$
Question
To construct a rectangle with adjacent sides $AB = 3\text{ cm}$ and $BC = 5\text{ cm}$, what type of triangle is constructed first?
Answer
A right-angled triangle.
Question
When only one side and one diagonal of a rectangle are given, the construction is completed by drawing two _____ triangles.
Answer
right-angled
Question
What is the defining property of the diagonals of a rhombus regarding their intersection?
Answer
They bisect each other at right angles ($90^{\circ}$).
Question
In constructing a rhombus from diagonals $AC$ and $BD$, what must be drawn to diagonal $AC$ to find the line for $BD$?
Answer
A perpendicular bisector.
Question
If a rhombus has diagonal $AC = 6.0\text{ cm}$ and $BD = 4.6\text{ cm}$, how far from the intersection point $O$ are the vertices $B$ and $D$ located?
Answer
$2.3\text{ cm}$
Question
The construction method for a square given its diagonal is identical to the method used for a _____.
Answer
rhombus
Question
What is the value of each interior angle in a regular hexagon?
Answer
$120^{\circ}$
Question
In Method 1 of constructing a regular hexagon, if side $AB = 3.0\text{ cm}$, what is the measure of $\angle PAB$?
Answer
$120^{\circ}$
Question
Method 2 for constructing a regular hexagon relies on the fact that the side length is equal to the _____ of its circumcircle.
Answer
radius
Question
When using Method 2 for a regular hexagon of side $3.0\text{ cm}$, how many times is the radius length marked along the circumference?
Answer
Six times.
Question
In Method 3 for a regular hexagon, what is the angle subtended by each side at the centre of the circumcircle?
Answer
$\frac{360^{\circ}}{6} = 60^{\circ}$
Question
Constructing an equilateral triangle $AOB$ inside a circle where $O$ is the centre is a step in constructing which polygon?
Answer
A regular hexagon.
Question
Can a quadrilateral be constructed if only four sides are known?
Answer
No, at least one more part (like an angle or diagonal) is required.
Question
Is it possible to construct a unique parallelogram if only the lengths of the two diagonals are given?
Answer
No, the angle between the diagonals is also required.
Question
True or False: A rhombus can be constructed if only the lengths of its two diagonals are known.
Answer
True
Question
If the diagonals of a quadrilateral are equal and bisect each other at right angles, the figure is a _____.
Answer
square
Question
In the construction of a parallelogram given two adjacent sides and an altitude, the altitude is the distance between _____ sides.
Answer
parallel
Question
To find the mid-point of a line segment using only a compass and ruler, one constructs a _____.
Answer
perpendicular bisector
Question
If a regular hexagon's leading diagonal is twice the length of its side, can it be constructed from the diagonal alone?
Answer
Yes.
Question
In a regular hexagon, opposite sides are always _____.
Answer
parallel
Question
When constructing a regular hexagon by dividing a circle, what is the relationship between the chord length and the radius?
Answer
They are equal.
Question
For a quadrilateral $ABCD$ to be constructed, the sum of any three angles must be less than _____.
Answer
$360^{\circ}$
Question
A trapezium can be constructed if four _____ are given.
Answer
sides
Question
How many degrees are in the sum of the interior angles of any quadrilateral?
Answer
$360^{\circ}$
Question
In a parallelogram $ABCD$, if $\angle A = 75^{\circ}$, what is the measure of the consecutive angle $\angle B$?
Answer
$105^{\circ}$
Question
To construct a rectangle $ABCD$ with $AB = 6.0\text{ cm}$ and $AD = 5.0\text{ cm}$, what angle must be constructed at vertex $A$?
Answer
$90^{\circ}$
Question
Which specific tool is used to draw arcs of a specific radius in geometric constructions?
Answer
A compass.
Question
In the construction of a parallelogram using diagonals $AC$ and $BD$ and an acute angle between them, if the angle is $60^{\circ}$, which angle at the intersection $O$ is $60^{\circ}$?
Answer
$\angle DOC$ (or $\angle AOB$).
Question
In the construction of a trapezium $ABCD$ where $AD \parallel BC$, if $AD = 3\text{ cm}$ and $BC = 5\text{ cm}$, what length is $EC$ if $BE = AD$?
Answer
$2\text{ cm}$
Question
To locate vertex $D$ in a quadrilateral construction where $CD = 5\text{ cm}$ and $DA = 4\text{ cm}$ are given, from which two points should arcs be drawn?
Answer
Points $C$ and $A$.
Question
When constructing a regular hexagon $ABCDEF$, why is it possible to use the radius of the circle to mark all vertices?
Answer
Because the hexagon is composed of six equilateral triangles meeting at the centre.
Question
What is the measure of the exterior angle of a regular hexagon?
Answer
$60^{\circ}$
Question
If the sides of a quadrilateral are $5\text{ cm}$, $6\text{ cm}$, $7\text{ cm}$, $8\text{ cm}$ and a diagonal is $15\text{ cm}$, why is construction impossible?
Answer
Because the diagonal is longer than the sum of two sides (violating the triangle inequality).
Question
In a rhombus $ABCD$, if diagonal $AC = 6.3\text{ cm}$ and $BD = 5.8\text{ cm}$, what is the distance from the intersection $O$ to vertex $A$?
Answer
$3.15\text{ cm}$
Question
Which property ensures that a rectangle can be constructed with just two adjacent sides given?
Answer
All angles are $90^{\circ}$ and opposite sides are equal.
Question
If the perimeter of a square is $24\text{ cm}$, what side length is used for construction?
Answer
$6\text{ cm}$
Question
To construct a parallelogram when two adjacent sides and the height corresponding to one side are given, which side is drawn first?
Answer
The side to which the height corresponds.
Question
In the construction of a regular hexagon by Method 1, after drawing side $AB$ and the $120^{\circ}$ angles at $A$ and $B$, which points are located next?
Answer
Points $F$ and $C$.
Question
A quadrilateral can be constructed if its four sides and one _____ are known.
Answer
angle (or diagonal)
Question
In a parallelogram, if $\angle DAB = 45^{\circ}$, what is the measure of the opposite angle $\angle BCD$?
Answer
$45^{\circ}$