Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

1. Construct an angle of 90° at the initial point of a given ray and justify the construction.

Given: A ray OA.
Required: To construct an angle of 90° at O and justify the construction.
Steps of Construction:
1. Taking O as centre and some radius, draw an arc of a circle, which intersects OA, say at a point B.
2. Taking B as centre and with the same radius as before, draw an are intersecting the previously drawn are, say at a point C.

Given: A ray OA.Required: To construct an angle of 90° at O and just

3. Taking C as centre and with the same radius as before, draw an arc intersecting the arc drawn in step 1, say at D.
4. Draw the ray OE passing through C. Then ∠EOA = 60°.
5. Draw the ray OF passing through D. Then ∠FOE = 60°.
6. Next, taking C and D as centres and with the radius more than $1 half$ ID, draw arcs to intersect each other, say at G.

7. Draw the ray OG. This ray OG is the bisector of the angle ∠FOE, i.e., ∠FOG

$equals angle EOG equals 1 half angle FOE equals 1 half left parenthesis 60 degree right parenthesis equals 30 degree Thus comma space space space angle GOA equals angle GOE plus angle EOA equals 30 degree plus 60 degree equals 90 degree$

Justification:
(i) Join BC.
Then. OC = OB = BC (By construction)
∴ ∆COB is an equilateral triangle.
∴ ∠COB = 60°.
∴ ∠EOA = 60°.
(ii) Join CD.
Then, OD = OC = CD (By construction)
∴ ∆DOC is an equilateral triangle.

$therefore space space space angle DOC equals 60 degree therefore space space space angle FOE equals 60 degree left parenthesis iii right parenthesis space space Join space CG space and space DG In space increment ODG space and space increment OCG comma OD space equals OC space space space space space space space space space space space space space space vertical line space Radii space fo space the space same space arc DG space equals space CG space space space space space space space space space space space space space space space vertical line space Arcs space of space equal space radi OG space equals space OG space space space space space space space space space space space space space space space space space space space space space space space space space space space vertical line space Common therefore increment ODG space approximately equal to space increment OCG space space space space space space space space space space space space space vertical line space SSS space Rule therefore space angle DOG equals angle COG space space space space space space space space space space space space space space space space space vertical line space CPCT therefore space space space space angle FOG equals angle EOG equals 1 half angle FOE space space space space space space space space space space space space space space space space equals space 1 half left parenthesis 60 degree right parenthesis equals 30 degree Thus comma space angle GOA equals angle GOE plus angle EOA space space space space space space space space space space space space space space space space space space equals space 30 degree plus 60 degree equals 90 degree$