Quick Review Flashcards - Click to flip and test your knowledge!
Question
What is the definition of a rectilinear figure?
Answer
A plane figure bounded by straight lines.
Question
A closed plane figure bounded by at least three line segments is known as a _____.
Answer
polygon
Question
What is the specific name for a polygon with 5 sides?
Answer
Pentagon
Question
What is the specific name for a polygon with 7 sides?
Answer
Heptagon
Question
A polygon is classified as _____ if every one of its interior angles is less than $180^{\circ}$.
Answer
convex
Question
What term describes a polygon that has at least one interior angle greater than $180^{\circ}$?
Answer
Concave polygon
Question
In general geometric contexts, what is assumed about a polygon unless stated otherwise?
Answer
It is a convex polygon.
Question
Formula: The sum of the interior angles of a polygon with $n$ sides (expressed in right angles).
Answer
$(2n - 4)$ right angles
Question
Formula: The sum of the interior angles of a polygon with $n$ sides (expressed in degrees).
Answer
$(n - 2) \times 180^{\circ}$
Question
Regardless of the number of sides, what is the sum of the exterior angles of any polygon produced in order?
Answer
$360^{\circ}$ (or 4 right angles)
Question
How is a 'regular polygon' defined?
Answer
A polygon in which all sides and all angles are equal.
Question
In any polygon, what is the sum of an interior angle and its adjacent exterior angle at a vertex?
Answer
$180^{\circ}$
Question
Formula: The measure of each interior angle of a regular polygon with $n$ sides.
Answer
$\frac{(2n - 4) \times 90^{\circ}}{n}$
Question
Formula: The measure of each exterior angle of a regular polygon with $n$ sides.
Answer
$\frac{360^{\circ}}{n}$
Question
If each exterior angle of a regular polygon is $x^{\circ}$, what is the formula for the number of sides $n$?
Answer
$n = \frac{360}{x}$
Question
In a regular polygon, as the number of sides increases, what happens to the value of each interior angle?
Answer
The value of each interior angle increases.
Question
In a regular polygon, as the number of sides increases, what happens to the value of each exterior angle?
Answer
The value of each exterior angle decreases.
Question
A closed plane figure bounded by four line segments is called a _____.
Answer
quadrilateral
Question
What is the sum of the interior angles of any quadrilateral?
Answer
$360^{\circ}$
Question
What defines a trapezium?
Answer
A quadrilateral in which one pair of opposite sides is parallel.
Question
What is an 'isosceles trapezium'?
Answer
A trapezium in which the non-parallel sides are equal in length.
Question
In an isosceles trapezium $ABCD$ where $AB \parallel DC$ and $AD = BC$, what is the relationship between $\angle D$ and $\angle C$?
Answer
$\angle D = \angle C$
Question
In an isosceles trapezium, what is the relationship between the lengths of the two diagonals?
Answer
The diagonals are equal ($AC = BD$).
Question
What is the definition of a parallelogram?
Answer
A quadrilateral in which both pairs of opposite sides are parallel.
Question
In a parallelogram, what is the relationship between opposite sides?
Answer
Opposite sides are equal in length.
Question
In a parallelogram, what is the relationship between opposite angles?
Answer
Opposite angles are equal.
Question
What is the sum of any two consecutive (conjoined) angles in a parallelogram?
Answer
$180^{\circ}$ (they are supplementary).
Question
How do the diagonals of a parallelogram interact with each other?
Answer
They bisect each other.
Question
Each diagonal of a parallelogram divides the figure into two _____ triangles.
Answer
congruent
Question
Into how many triangles of equal area do the diagonals of a parallelogram divide the figure?
Answer
Four
Question
A parallelogram in which every angle is a right angle is called a _____.
Answer
rectangle
Question
What is unique about the diagonals of a rectangle compared to a general parallelogram?
Answer
The diagonals of a rectangle are equal in length.
Question
A parallelogram in which all four sides are equal is called a _____.
Answer
rhombus
Question
At what angle do the diagonals of a rhombus bisect each other?
Answer
$90^{\circ}$ (right angles).
Question
How do the diagonals of a rhombus affect the interior angles at the vertices?
Answer
Each diagonal bisects the angles at the vertices it joins.
Question
A parallelogram with all sides equal and each angle equal to $90^{\circ}$ is a _____.
Answer
square
Question
At what angle do the diagonals of a square bisect each other?
Answer
$90^{\circ}$ (right angles).
Question
Property Comparison: Which quadrilaterals have diagonals that are always equal in length?
Answer
Rectangle and Square.
Question
Property Comparison: Which quadrilaterals have diagonals that intersect at right angles?
Answer
Rhombus and Square.
Question
Property Comparison: Which quadrilaterals have diagonals that bisect vertex angles?
Answer
Rhombus and Square.
Question
Theorem 11 states that in a parallelogram, both pairs of _____ are equal.
Answer
opposite sides
Question
According to Theorem 12, what is true about the opposite angles of a parallelogram?
Answer
They are equal.
Question
Theorem 13: A quadrilateral is a parallelogram if one pair of opposite sides are both _____ and _____.
Answer
equal; parallel
Question
Theorem 15: The diagonals of a parallelogram _____ each other.
Answer
bisect
Question
Which theorem states that a rhombus is a special parallelogram whose diagonals meet at right angles?
Answer
Theorem 16
Question
Theorem 17 states that in a rectangle, the diagonals are _____.
Answer
equal
Question
According to Theorem 18, the diagonals of a square are _____ and meet at _____.
Answer
equal; right angles
Question
If the diagonals of a quadrilateral bisect each other, the quadrilateral is a _____.
Answer
parallelogram
Question
True or False: Every rhombus is a parallelogram.
Answer
True
Question
True or False: Every rectangle is a square.
Answer
False
Question
True or False: Every square is a rhombus.
Answer
True
Question
If the diagonals of a parallelogram are equal, the figure is a _____.
Answer
rectangle
Question
If the diagonals of a parallelogram intersect at right angles, the figure is a _____.
Answer
rhombus
Question
If the diagonals of a rhombus are equal, the figure is a _____.
Answer
square
Question
What angle does the diagonal of a square make with its sides?
Answer
$45^{\circ}$
Question
In a parallelogram $ABCD$, if $\angle A = 70^{\circ}$, what is the measure of $\angle B$?
Answer
$110^{\circ}$
Question
In a rhombus, if one diagonal is equal to a side, the rhombus is composed of two _____ triangles.
Answer
equilateral
Question
If the ratio between an exterior angle and an interior angle of a regular polygon is $2 : 3$, how many sides does it have?
Answer
5
Question
Formula: The number of diagonals that can be drawn from one vertex of an $n$-sided polygon.
Answer
$n - 3$
Question
A quadrilateral in which only one pair of opposite sides is parallel is a _____.
Answer
trapezium