Theorem : if two angles of a triangle are unequal then the side opposite to the greater angle is greater than the side opposite to smaller angle.the theorem can the proved by indirect proof. Complete the following proof by filling in the blanks
Given : in triangle ABC , Angle B greater than angle C
To prove : AC greater than AB
Proof : there are only three possibilities regarding the length of side AB and side AC of triangle ABC
(i) AC less then AB (ii)
(iii)
(i) let us assume mean that AC less than AB
if two sides of a triangle are unequal then the angle opposite to greater side is .............. .
.
. . angle C greater than ..........
but angle C less than angle B .......(given)
this creates a contradiction
thatis ........... less than ...........is wrong
(ii) if AC = AB
then Angle B = Angle C
but..........greater than ...........(given)
these also creates a contradiction.
that is ......... = ..........is wrong
that is AC greater than ab is the only remaining possibility.
that is.AC greater than AB .
Answers
Answer:
PROVED
Step-by-step explanation:
Given : in triangle ABC , Angle B greater than angle C
To prove : AC greater than AB
Proof : there are only three possibilities regarding the length of side AB and side AC of triangle ABC
(i) AC less then AB (ii) AC=AB
(iii)AC>AB
(i) let us assume mean that AC less than AB
if two sides of a triangle are unequal then the angle opposite to greater side is greater .
.
. . angle C greater than angle B.
but angle C less than angle B (given)
this creates a contradiction
thatis angle B less than angle C is wrong
(ii) if AC = AB
then Angle B = Angle C
but Angle B is greater than Angle C (given)
these also creates a contradiction.
that is Angle B = Angle C is wrong
that is AC greater than ab is the only remaining possibility.
that is.AC greater than AB .
#SPJ3
Step-by-step explanation:
Theorem : if two angles of a triangle are unequal then the side opposite to the greater angle is greater than the side opposite to smaller angle.the theorem can the proved by indirect proof. Complete the following proof by filling in the blanks
Given : in triangle ABC , Angle B greater than angle C
To prove : AC greater than AB
Proof : there are only three possibilities regarding the length of side AB and side AC of triangle ABC
(i) AC less then AB (ii)
(iii)
(i) let us assume mean that AC less than AB
if two sides of a triangle are unequal then the angle opposite to greater side is greater
.
. . angle C greater than B
but angle C less than angle B .......(given)
this creates a contradiction
that is angle B less than angle C is wrong
(ii) if AC = AB
then Angle B = Angle C
but angle B greater than angle C.....(given)
these also creates a contradiction.
that is angle B = angle C is wrong
that is AC greater than ab is the only remaining possibility.
that is.AC greater than AB .
