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Standard VII

Mathematics

Exterior Angle of a Triangle and Its Property

State true or...

Question

State true or false:

The sides $A B$ and $A C$ of a triangle $A B C$ are produced; and the bisectors of the external angles at $B$ and $C$ meet at $P$ . Now if $A B > A C$ , then $P C > P B$

If true enter 1 else 0

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Solution

here, $A B > A C$
As we know, $A$ greater angle of a triangle is opposite a greater side.
So, $∠ A C B > ∠ A B C$
and external angle will be smaller.
So, $∠ B C F < ∠ C B E$
$\frac{1}{2} ∠ B C F < \frac{1}{2} ∠ C B E$
$∠ B C P < ∠ C B P$
As $A$ is greater angle of a triangle is opposite a greater side.
So, $P C > P B$

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Similar questions

The sides AB and AC of a triangle ABC are produced; and the bisectors of the external angles at B and C meet at P Now if AB >
AC, then PC < PB.

If the above statement is true then mention answer as 1, else mention 0 if false

Q. The sides

A B

and

A C

of a triangle

A B C

are produced; and the bisectors of the external angles at

B

and

C

meet at

P

. Prove that if

A B > A C

, then

P C > P B

Q. State true or false:

In isosceles triangle

A B C

, sides

A B

and

A C

are equal. If midpoint

D

lies in base

B C

and point

E

lies on

B C

produced (BC being produced through vertex C), then

A C > A D

If true enter 1 else 0

Q. State true or false:

The side

A C

of a triangle

A B C

is produced to point

E

so that

C E = \frac{1}{2} A C

D

is the mid-point of

B C

and

E D

produced meets

A B

F

. Lines through

D

and

C

are drawn parallel to

A B

which meet

A C

at point

P

and

E F

at point

R

respectively. Hence,

4 C R = A B

State that whether given statement is true or false

The sides AB and AC of

Δ A B C

are produce to D and E respectively and the bisectors of

∠ C B D

and

∠ B C D

meet at

O

A B > A C

, prove that

O C > O B

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State true or false:The sides AB and AC of a triangle ABC are produced; and the bisectors of the external angles at B and C meet at P. Now if AB>AC, then PC>PBIf true enter 1 else 0

here, AB>ACAs we know, A greater angle of a triangle is opposite a greater side.So, ∠ACB>∠ABCand external angle will be smaller.So, ∠BCF<∠CBE12∠BCF<12∠CBE∠BCP<∠CBPAs A is greater angle of a triangle is opposite a greater side.So, PC>PB

State true or false:

The sides $A B$ and $A C$ of a triangle $A B C$ are produced; and the bisectors of the external angles at $B$ and $C$ meet at $P$ . Now if $A B > A C$ , then $P C > P B$

If true enter 1 else 0