In a parallelogram, opposite sides are equal. - Vidyadip

Question

In a parallelogram, opposite sides are equal.

✓

Answer

You have already proved that a diagonal divides the parallelogram into two congruent triangles; so what can you say about the corresponding sides? They are equal. gparts say, 1 the corresponding
So, AB DC and AD = BC
Now what is the converse of this result? You already know that whatever is given in a theorem, the same is to be proved in the converse and whatever is proved in the theorem it is given in the converse. Thus, Theorem 8.2 can be stated as given below:
If a quadrilateral is a parallelogram, then each pair of its opposite sides is equal. So its converse is:

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Quadrilaterals→Quadrilaterals — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Ravish tells his doughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be".. lf present ages of Aarushi and Ravish are $x$ and $y$ years respectively, represent this situation algebraically as well as graphically.

In $\triangle\text{ABC,}$ side $AB$ is produced to $D$ such that $BD = BC$. If $\angle\text{B}=60^{\circ},$ and $\angle\text{B}=60^{\circ},$ prove that:
$i. AD > CD$ and
$ii. AD > AC$.

$AB$ and $CD$ are respectively the smallest and largest sides of a quadrilateral $\text{ABCD}$. Show that $\angle\text{A}>\angle\text{C}$ and $\angle\text{B}>\angle\text{D}.$

Calculate the area of the triangle whose sides are $18\ cm, 34\ cm, 24\ cm$ and $30\ cm$ in length. Also, find the length of the altitude corresponding to the smallest side.

Following are the ages $($in years$)$ of $360$ patients, getting medical treatment in a hospital:

Age $($in years$)$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Number of patients	$90$	$50$	$60$	$80$	$50$	$30$

One of the patients is selected at random. What is the probability that his age is:
$i. 30$ years or more but less than $40$ years$?$
$ii. 50$ years or more but less than $70$ years$?$
$iii.10$ years or more but less than $40$ years$?$
$iv. 10$ years or more$?$
$v.$ Less than $10$ years$?$

$M$ is a point on side $BC$ of a triangle $ABC$ such that $AM$ is the bisector of $\angle\text{BCA}.$ Is it true to say that perimeter of the triangle is greater than $2AM?$ Give reason for your answer$?$

Plot the points $A(1, -1)$ and $B(4, 5):$
$i.$ Draw a line segment joining these points. Write the coordinates of a point on this line segment between the points $A$ and $B.$
$ii.$ Extend this line segment and write the coordinates of a point on this line which lies outside the line segment $AB.$

In the given figure, $O$ is a point in the interior of square $ABCD$ such that $\triangle\text{OAB}$ is an equilateral triangle. Show that $\triangle\text{OCD}$ is an isosceles triangle.

Given below are the seats won by different political parties in the polling outcome of a state assembly elections:

Political party	$A$	$B$	$C$	$D$	$E$	$F$
Seats won	$75$	$55$	$37$	$29$	$10$	$37$

$i.$ Draw a bar graph to represent the polling results.
$ii.$ Which political party won the maximum number of seats$?$

Show that the quadrilateral formed by joining the midpoints of the pairs of adjacent sides of a rectangle is a rhombus.