If two arcs are congruent, then their corresponding chords are equal. true or false?

Learn more about Angles, Arcs, and Chords and Tangents

Recommended textbooks for you

Elementary Geometry For College Students, 7e

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Elementary Geometry for College Students

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Cengage Learning

Elementary Geometry For College Students, 7e

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Cengage,

Elementary Geometry for College Students

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Cengage Learning

In a circle if two chords are congruent then their corresponding are congruent.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Text Solution

Solution : Let AXB and CYD are arcs of circle whose centre and radus are O and r units, respectively. <br> So, OA=OB=OC=OD=r …..(i) <br> `:' "arc "AXB cong"arc "CYD` <br> ` :. angle AOB=angleCOD ` <br> [congruent arcs of a circle subtend equal angles at the centre] <br> In `DeltaAOB abd DeltaCOD`, <br> AO=CO [form Eq. (i)] <br> BO=DO [from Eq.(i)] <br> `angle AOB=angleCOD` [from Eq. (ii)] <br> `:.Delta AOB cong Delta COD`[by SAS songruence rule] <br> `rArr AB=CD` [by COCT] <br> `rArr (AB)/(CD)=1` <br> the ratio of AB and CD is `1 : 1`.