1 OBJECTIVE QUESTIONS and

the nodal points are conjugate points in the object and image space with unity angular magnification The planes normal to the axis that contain the nodal points are called the nodal planes If n1=n2 then the nodal planes coincide with the principle planes The usefulness of the cardinal points is best illustrated with some specific examples

Coordinate Geometry - Brillantmont Mathematics

The diagram shows a rhombus ABCD The points B and D have coordinates (2, 10) and (6, 2) respectively, and A lies on the x-axis The mid-point of BD is M Find, by

33 In the figure below, ABCD is a square Points are chosen

Jan 31, 2014 · 33 In the figure below, ABCD is a square Points are chosen on each pair of adjacent sides of ABCD to form 4 congruent right triangles, as shown below

Thick Lenses and the ABCD Formalism

points where parallel incident rays would intersect converging exiting rays There is a primary (on the front side) and a secondary (on the back side) principle plane These are located a distance h 1 and h 2 from the vertices These distances are positive when the plane is to the right of the vertex

Mid- Year Exam key

Which transformation on quadrilateral ABCD produces an image that does not preserve distance between points in quadrilateral ABCD? B c D reflection across y = x

GSRTB5: Quadrilateral Proofs - JMAP

Regents Exam Questions G SRT B 5: Quadrilateral Proofs Name: _____ www jmap 3 12 In quadrilateral ABCD, AB ≅CD, AB CD, and BFand DE are perpendicular to

GCOC11: Quadrilateral Proofs - mailjmaporg

ID: A 1 G CO C 11: Quadrilateral Proofs Answer Section 1 ANS: 2 REF: 011411ge 2 ANS: Because ABCD is a parallelogram, AD CB and since ABE is a transversal, ∠BAD and

Mid-point and Intercept Theorems 1 In ABC, D is the mid

FRANK Solutions Class 9 Maths Chapter 15 Mid-point and Intercept Theorems = 4 5 cm 3 (a) In ABC, D, E, F are the mid-points of BC, CA and AB respectively Find FE, if

1 OBJECTIVE QUESTIONS and

Chap 9 : Areas of Parallelograms and Triangles www rava in Get all GUIDE and Sample Paper PDFs by whatsapp from +91 89056 29969 Page 61

[PDF] abcd est un tétraèdre i est le milieu de ad

[PDF] abcd est un tétraèdre tel que ab=cd ad=bc ac=bd

[PDF] construire la section du cube par le plan (ijk)

[PDF] pondichery 2017 maths

[PDF] demontrer que le vecteur ce est un vecteur normal au plan ijk

[PDF] géométrie dans l'espace exercices corrigés

[PDF] abcdefgh est un cube i est le milieu de ae

[PDF] soit un cube abcdefgh d arête 1

[PDF] déterminer les coordonnées du point h intersection de la droite d et du plan abc

[PDF] abdos pro pdf

[PDF] programme abdos efficace

[PDF] exercice abdominaux homme sans materiel

[PDF] programme abdominaux homme 1 mois

[PDF] programme musculation abdominaux pdf

[PDF] exercices de gainage musculaire pdf

Chap 9 : Areas of Parallelograms and Triangles www.rava.org.in Get all GUIDE and Sample Paper PDFs by whatsapp from +91 89056 29969 Page 61

CHAPTER CHAPTER 99

1. OBJECTIVE QUESTIONS

1. Area of an isosceles triangle, the measure of one of its

equal side being 5 cm and the third side 4 cm is (a) cm221 2 (b) cm21 2 2 (c) cm22 3 2 (d) cm23 3 2

Ans : (a) cm221

Let, a cm5, cmb4

Therefore area of an isosceles triangle

bab4422 .sq cm4442516# cm84 .sq cm221

2. In the given figure, ABCD is a parallelogram, then

area ()AFBT is (a) cm16 2 (b) cm8 2 (c) cm4 2 (d) cm6 2

Ans : (b) cm8

2 ()areaAFBT ()area gmABCD21z

2144##

cm8 2

3. X and Yare respectively two points on the sides DC

and

AD of the parallelogram ABCD. The area of

ABXT is equal to :

(a) /13# area of BYCT (b) area of BYCT (c) /12# area of BYCT (d) 2# area of BYCT

Ans : (b) area of BYCT

4. BD is a median of a triangle ABC. F is a point on

AB such that CE intersects BD at E and .BE ED

If cmBF5, BA is equal to: (a) 10 (b) 12 (c) 15 (d) 17

Ans : (c) 155.

D and E are the mid points of the sides AB and AC

of a triangle ABC respectively. Then the area of the triangles

ADE and ABC are in the ratio

(a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 2 : 3

Ans : (c) 1 : 4

6. In

ABCT if D is a point on BC and divides it in the

ratio :35 i.e. if ::BD DC35, then area ():()arADC ABCTT (a) 3 : 5 (b) 3 : 8 (c) 5 : 8 (d) 8 : 3

Ans : (c) 5 : 8

7. The area of a rhombus is

cm20 2 . If one of its diagonals is 5 cm, the other diagonal is (a) 5 cm (b) 6 cm (c) 8 cm (d) 10 cm

Ans : (c) 8 cm

Area of rhombus

2112##; where d

1 , d 2 are lengths of diagonals.

20 d215

2## [Since, d5

1 d 2 cm8

8. The area of trapezium PQRS in the adjoining figure

is (a) cm112 2 (b) cm120 2 (c) cm160 2 (d) cm180 2

Ans : (d) cm180

2 (. )area trapPQRS (. ) ( )area rect areaPSRT QRTT ()PT RT QT RT21## ()RT RT8218## ...(1) RT12#

Now, in QRTT,

RT 2 QR QT 22

File Revision Date :

For NCERT Solutions Previous Years Chapterwise QB

visit www.cbse.online or whatsapp at 8905629969 Download all GUIDE and Sample Paper pdfs from www.cbse.online or www.rava.org.in Page 62 Chap 9 : Areas of Parallelograms and Triangles www.cbse.online 17 8 22

RT cm15

Substitute the value of

RT in (1), we get

(. )area trapPQRS cm12 15 2 # cm180 2

9. In the figure, ABCD is a quadrilateral cmBD20. If

AL BD= and CM BD= such that AL10 cm and

CM 5 cm, find the area of quad. ABCD.

(a) 150 cm 2 (b) 180 cm 2 (c) 100 cm 2 (d) 140 cm 2

Ans : (a) 150 cm

Area of quad. ABCD ()()area areaABD BCDTT

BD AL BD CM2121## ##

2120 102120 5## ##

100 50 cm150

10. The area of a rhombus if the lengths of whose diagonals

are 16 cm and 24 cm, is (a) 180 cm 2 (b) 184 cm 2 (c) 198 cm 2 (d) 192 cm 2

Ans : (d) 192 cm

Area of rhombus dd21

12## cm2116 24 2 ## cm192 2

11. In the adjoining figure, ABCD is a parallelogram.

Then its area is equal to

(a) cm9 2 (b) cm12 2 (c) cm15 2 (d) cm36 2

Ans : (b) cm12

Area of parallelogram Base # Height

AB BD# cm43

2 cm12 2

12. Which of the following figures lie on the same base

and between the same parallels? (a) (b) (c) (d) All of these

Ans : (b)

Common base

DC and two parallels are AB and DC

13. The area of a trapezium whose parallel sides are 9

cm & 16 cm and the distance between these sides is

8 cm, is

(a) 60 cm 2 (b) 72 cm 2 (c) 56 cm 2 (d) 100 cm 2

Ans : (d) 100 cm

Area of trapezium ABCD

[]AB CD AE21# []cm2116 9 8 2 cm2125 8 2 ## cm100 2

14. In the adjoining figure, ABCD is a quadrilateral

in which diagonal cmBD14. If AL BD= and

CM BD= such that cmAL8 and cmCM6,

then area of quadrilateral

ABCD is

(a) 60 cm 2 (b) 72 cm 2quotesdbs_dbs11.pdfusesText_17

[PDF] 1 OBJECTIVE QUESTIONS and