Math, asked by ram32646, 8 months ago

5. Explain why a rectangle is a convex quadrilateral.
D
6. ABC is a right-angled triangle and O is the mid point of the side
opposite to the right angle. Explain why O is equidistant from A,
B and C. (The dotted lines are drawn additionally to help you).
B
C​

Answers

Answered by sutapathakur2008
1

Answer:

ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A, B, and C. (The dotted lines are drawn additionally to help you).

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ANSWER

Between Δ AOD & Δ BOC we have AO=CO (given),BO=OD (by Construction).

∠ AOD =∠ BOC....Vertically opposite angle

∴ By SAS test Δ AOD & Δ BOC are congruent.

So AD=BC....(i)

similarly, between Δ AOB & Δ DOC we have AO=CO (given), BO=OD (by Construction)

∠ AOB =∠ DOC

∴ By SAS test Δ AOB & Δ DOC are congruent.

So AB=DC.....(ii)

Also ∠ ABC=90

o

....(iii)

∴ From (i) & (ii) & (iii) we conclude that ABCD is a rectangle.

So the diagonals AC & BD are equal and bisect each other at O.

∴ OA=OB=OC=OD.

i.e O is equidistant from A, B & C.

Step-by-step explanation:

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Answered by parul4747
1

ANSWER

ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A, B, and C. (The dotted lines are drawn additionally to help you).

8415

ANSWER

Between Δ AOD & Δ BOC we have AO=CO (given),BO=OD (by Construction).

etween Δ AOD & Δ BOC we have AO=CO (given),BO=OD (by Construction).∠ AOD =∠ BOC....Vertically opposite angle

etween Δ AOD & Δ BOC we have AO=CO (given),BO=OD (by Construction).∠ AOD =∠ BOC....Vertically opposite angle∴ By SAS test Δ AOD & Δ BOC are congruent.

etween Δ AOD & Δ BOC we have AO=CO (given),BO=OD (by Construction).∠ AOD =∠ BOC....Vertically opposite angle∴ By SAS test Δ AOD & Δ BOC are congruent.So AD=BC....(i)

similarly, between Δ AOB & Δ DOC we have AO=CO (given), BO=OD (by Construction)

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.So AB=DC.....(ii)

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.So AB=DC.....(ii)Also ∠ ABC=90

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.So AB=DC.....(ii)Also ∠ ABC=90 o

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.So AB=DC.....(ii)Also ∠ ABC=90 o ....(iii)

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.So AB=DC.....(ii)Also ∠ ABC=90 o ....(iii)∴ From (i) & (ii) & (iii) we conclude that ABCD is a rectangle.

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.So AB=DC.....(ii)Also ∠ ABC=90 o ....(iii)∴ From (i) & (ii) & (iii) we conclude that ABCD is a rectangle.So the diagonals AC & BD are equal and bisect each other at O.

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.So AB=DC.....(ii)Also ∠ ABC=90 o ....(iii)∴ From (i) & (ii) & (iii) we conclude that ABCD is a rectangle.So the diagonals AC & BD are equal and bisect each other at O.∴ OA=OB=OC=OD.

AO=CO (given), BO=OD (by Construction)∠ AOB =∠ DOC∴ By SAS test Δ AOB & Δ DOC are congruent.So AB=DC.....(ii)Also ∠ ABC=90 o ....(iii)∴ From (i) & (ii) & (iii) we conclude that ABCD is a rectangle.So the diagonals AC & BD are equal and bisect each other at O.∴ OA=OB=OC=OD. i.e O is equidistant from A, B & C.

Hope it will help you

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