Quick Review Flashcards - Click to flip and test your knowledge!
Question
How is the area of a plane figure defined?
Answer
The region bounded by the figure.
Question
What is the relationship between the areas of two congruent figures?
Answer
They are always equal in area.
Question
Is it always true that figures with equal areas are congruent?
Answer
No, the converse of the congruency-area rule is not always true.
Question
When are figures said to be 'between the same parallels'?
Answer
When their bases lie on the same straight line and their opposite vertices lie on a parallel straight line.
Question
Figures between the same parallels always have equal _____.
Answer
Altitudes.
Question
What is the formula for the area of a parallelogram?
Answer
$Base \times height$
Question
What is the formula for the area of a triangle?
Answer
$\frac{1}{2} \times base \times height$
Question
According to Theorem 19, parallelograms on the same base and between the same parallels are _____.
Answer
Equal in area.
Question
What is the relationship between a parallelogram and a rectangle on the same base and between the same parallels?
Answer
They are equal in area.
Question
Theorem 20: The area of a triangle is _____ the area of a parallelogram on the same base and between the same parallels.
Answer
Half
Question
Theorem 21: Triangles on the same base and between the same parallels are _____.
Answer
Equal in area.
Question
If two parallelograms stand on equal bases and lie between the same parallels, how do their areas compare?
Answer
They are equal in area.
Question
How does the area of a triangle compare to a parallelogram on an equal base and between the same parallels?
Answer
The area of the triangle is half that of the parallelogram.
Question
Under what condition regarding base and area will two triangles have equal corresponding altitudes?
Answer
They must have equal areas and stand on the same base (or equal bases).
Question
In the proof of Theorem 19, what criterion is used to prove $\triangle ADF \cong \triangle BCE$?
Answer
$A.S.A.$ (Angle-Side-Angle).
Question
What effect does a diagonal have on the area of a parallelogram?
Answer
It bisects the parallelogram into two triangles of equal area.
Question
If a point $P$ lies inside a parallelogram $ABCD$, what is $Area(\triangle APB) + Area(\triangle CPD)$ equal to?
Answer
$\frac{1}{2} Area(Parallelogram \ ABCD)$
Question
Into what does a median divide a triangle?
Answer
Two triangles of equal area.
Question
If $AD$ divides base $BC$ of $\triangle ABC$ in the ratio $m:n$, what is the ratio of $Area(\triangle ABD)$ to $Area(\triangle ADC)$?
Answer
$m:n$
Question
Triangles with the same vertex and bases along the same line have areas in the ratio of their _____.
Answer
Bases.
Question
In $\triangle ABC$, if point $D$ on side $BC$ results in $2BD = 3DC$, what is the ratio of $Area(\triangle ABD)$ to $Area(\triangle ABC)$?
Answer
$\frac{3}{5}$
Question
In parallelogram $ABCD$, if points $P$ and $Q$ trisect side $BC$, what is $Area(\triangle APQ)$ relative to the parallelogram?
Answer
$\frac{1}{6} Area(Parallelogram \ ABCD)$
Question
For a quadrilateral $ABCD$ with diagonals intersecting at $O$, what is the product $Area(\triangle AOD) \times Area(\triangle BOC)$ equal to?
Answer
$Area(\triangle AOB) \times Area(\triangle COD)$
Question
If $BD : DC = 3 : 5$ in $\triangle ABC$, what is the ratio $Area(\triangle ABD) : Area(\triangle ACD)$?
Answer
$3 : 5$
Question
What is the relationship between $Area(\triangle AOD)$ and $Area(\triangle BOC)$ in a trapezium where $AB \parallel DC$ and diagonals intersect at $O$?
Answer
They are equal in area.
Question
If $E$ is the mid-point of side $BC$ in $\triangle ABC$, how does $Area(\triangle BEA)$ compare to $Area(\triangle CEA)$?
Answer
They are equal in area.
Question
In $\triangle ABC$, if $AD$ is the median and $E$ is the midpoint of $AD$, then $Area(\triangle ABE) = \dots Area(\triangle ABC)$.
Answer
$\frac{1}{4}$
Question
If $ABCD$ is a parallelogram and $P$ and $Q$ are midpoints of $AB$ and $AD$, what is the area of $\triangle APQ$ relative to the parallelogram?
Answer
$\frac{1}{8}$ of the area of the parallelogram.
Question
If $BC$ of $\triangle ABC$ is divided at $D$ such that $BD = \frac{1}{2}DC$, what fraction of $Area(\triangle ABC)$ is $Area(\triangle ABD)$?
Answer
$\frac{1}{3}$
Question
In parallelogram $ABCD$, if $DP : PC = 3 : 2$, what is the ratio of $Area(\triangle DPB)$ to $Area(\triangle BPC)$?
Answer
$3 : 2$
Question
In a trapezium with parallel sides $a$ and $b$, the median line joining midpoints of non-parallel sides divides it into two trapeziums with area ratio _____.
Answer
$(3a + b) : (a + 3b)$
Question
In parallelogram $ABCD$, if $E$ is a point on $AB$ such that $AE : EB = 4 : 5$, what is the ratio of $Area(\triangle ADE)$ to $Area(\triangle ADB)$?
Answer
$4 : 9$
Question
What is the relationship between the areas of $\triangle ADE$ and quadrilateral $ABCD$ if $CE$ is drawn parallel to diagonal $DB$ of quadrilateral $ABCD$?
Answer
They are equal in area.
Question
Assertion: $PQRS$ is a parallelogram with area $180 \text{ cm}^2$. If $A$ is any point on diagonal $PR$, what is the area of $\triangle ASR$?
Answer
$45 \text{ cm}^2$
Question
If the perimeter of $\triangle ABC$ is $37 \text{ cm}$ and altitudes are in ratio $6 : 5 : 4$, the ratio of the lengths of its sides is _____.
Answer
$\frac{1}{6} : \frac{1}{5} : \frac{1}{4}$ (or $10 : 12 : 15$)
Question
The ratio of the areas of two triangles on the same base is equal to the ratio of their _____.
Answer
Heights.
Question
The ratio of the areas of two triangles of the same height is equal to the ratio of their _____.
Answer
Bases.
Question
In parallelogram $ABCD$, if $P$ and $Q$ are midpoints of $BC$ and $CD$, then $Area(\triangle APQ)$ is _____ of $Area(Parallelogram \ ABCD)$.
Answer
$\frac{3}{8}$
Question
A line through the vertex $A$ of $\triangle ABC$ meets $BC$ at $D$ and the median through $B$ at $E$. If $AE : ED = 2 : 1$, then $D$ is the _____ of $BC$.
Answer
Midpoint.
Question
If the medians of $\triangle ABC$ intersect at $G$, then $Area(\triangle BGC)$ is equal to _____ $Area(\triangle ABC)$.
Answer
$\frac{1}{3}$
Question
In $\triangle ABC$, if $G$ is the centroid, then $Area(\triangle AGB) = Area(\triangle BGC) = \dots$
Answer
$Area(\triangle AGC)$
Question
If $ABCD$ is a parallelogram, any line through the intersection of its diagonals divides the parallelogram into two parts of _____ area.
Answer
Equal
Question
In a parallelogram $ABCD$, if $P$ is the midpoint of $DC$, how does $Area(\triangle APB)$ relate to the area of the parallelogram?
Answer
It is half the area of the parallelogram.
Question
Theorem: If two triangles have equal base and equal area, they lie between the _____ parallels.
Answer
Same
Question
In $\triangle ABC$, if $D$ and $E$ are points on $AB$ and $AC$ such that $DE \parallel BC$, then $Area(\triangle BCD)$ is _____ $Area(\triangle BCE)$.
Answer
Equal to
Question
How does the area of a rectangle compare to a parallelogram if they have the same base and the same height?
Answer
They are equal in area.
Question
In quadrilateral $ABCD$, if $AC$ bisects $BD$, then $Area(\triangle ABC) = \dots$
Answer
$Area(\triangle ADC)$
Question
If the ratio of altitudes of a triangle is $a:b:c$, the ratio of the corresponding sides is _____.
Answer
$\frac{1}{a} : \frac{1}{b} : \frac{1}{c}$
Question
A median of a triangle divides it into two triangles of equal area because they have the same _____ and equal _____.
Answer
Altitude; bases.
Question
What is the area of a square with side $DA = 16 \text{ cm}$?
Answer
$256 \text{ cm}^2$
Question
If $E, F, G, H$ are mid-points of the sides of parallelogram $ABCD$, then $Area(EFGH)$ is _____ $Area(ABCD)$.
Answer
Half