Theorem 1: Parallelograms
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PQ and RS are two equal and parallel line segments.
Any point M not lying on PQ or RS is joined to Q and S and lines through P parallel to QM and through R parallel to SM meet at N . Prove that line segments MN and PQ are equal and parallel to each other.
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/27207/content_70.png)
- Area(ΔLZY)=Area(MZYX)
- Area(ΔNMX)=Area(MZYX)
- None of these
- Area(ΔLZN)=Area(MZYX)
In ABC , Given that DE//BC , D is the midpoint of AB and E is a midpoint of AC. The ratio AE : EC is ____.
1 : 1
1 : 3
1 : 2
2 : 1
- 1:3
- 1:1
- 1:2
- 2:1
Parallelograms an equal bases and between the same parallels are equal in area
False
True
If parallelogram ABCD and rectangle ABEM are of equal area, then:
Perimeter of AMEB = Perimeter of ADCB
Perimeter of AMEB
Perimeter of ADCB
Perimeter of AMEB
Perimeter of ADCB
Perimeter of AMEB =
Perimeter of ADCB
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
![](https://search-static.byjusweb.com/question-images/byjus/_29dacb2e1f9fb35620f1a2cf5293861fad941e3c20160919-21560-nes1zm.png)
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1480722/original_3-229.png)
and are points on sides and respectively of such that . Prove that
![](https://search-static.byjusweb.com/question-images/byjus/infinitestudent-images/ckeditor_assets/pictures/26433/content_capture.png)
- 30m
- 39m
- 32m
- 38m
Two photos are similar. The ratio of the corresponding side lengths is . What is the ratio of the areas?
The playing surfaces of two foosball tables are similar. The ratio of the corresponding side lengths is . What is the ratio of the areas?
In the given figure, PQRS is a rectangle of area 35cm2. Find the area of ΔEFT.
- 35cm2
- 70cm2
- 17.5cm2
- 60cm2
- 1 : 2
- 1 : 1
- 2 : 1
- 3 : 1
- double
- intersecting
- parallel
- equal
In the given figure, ABQP and ABCD are two parallelograms on the same base AB. Area of parallelogram ABCDArea of triangle PAB is equal to:
In the given figure area of Δ DAC is 60 cm2. Find the area of parallelogram ABCD.
[2 Marks]
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/203255/content_631164.png)
Find the value of the ratio (red to blue) of the areas of the similar figures.
The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/10962/content_1.png)
ar(ABCD) = ar(PBQR).
[Hint : Join AC and PQ. Now compare ar(ACQ) and ar(APQ).]
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1486297/original_5-28.png)
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/10962/content_1.png)
ΔAPB≅ΔCQD
![](https://s3-us-west-2.amazonaws.com/infinitestudent-images/ckeditor_assets/pictures/10962/content_1.png)
ΔAPB≅ΔCQD
- 1:2
- 3:1
- 1:4
- 1:3
![](https://infinitestudent-migration-images.s3-us-west-2.amazonaws.com/_d13bb96601905f978cc60b2f0342841b7775d4cf20160919-21560-eb82db.png)
Identify the incorrect statement from the following.
ΔAPD≅ΔCQB
AP = CQ
ΔAQB≅ΔCPD
AD = CQ
The area of parallelogram ABCD is:
- AB×BM
- BC×BN
- DC×DL
- AD×BM
Which among the following is correct?
Parallelograms on the same base and between the same set of parallel lines:
have unequal areas
have the same perimeter
may have equal or unequal areas
have equal areas
- equal
- double
- parallel
- intersecting
- 25.5 cm2
- 11.9 cm2
- 12.5 cm2
- 51 cm2