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Standard VIII

Mathematics

The Orthocentre

In Δ PQR, s...

Question

In $Δ$ PQR, seg PM is a median of $Δ$ PQR. Bisectors of $∠$ PMQ and $∠$ PMR intersect side PQ and PR at X and Y respectively. Show that $Δ$ PQR is similar to $Δ$ PXY.

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Solution

$\begin{matrix} ∠ Q M P + ∠ P M R = 180^{\circ} L . p a i r ∠ P X Y + ∠ Q X Y = 180^{\circ} {L . P} ∠ P Y X + ∠ R Y X = 180^{\circ} \end{matrix}$
Sum of angle formed but 0 is $180^{\circ}$
1.e L.P {Axioro}

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Similar questions

Q. In ∆PQR seg PM is a median. Angle bisectors of ∠PMQ and ∠PMR intersect side PQ and side PR in points X and Y respectively. Prove that XY || QR.

Q. Sides

A B

and

A C

and median

A D

of a

Δ

ABC are respecting proportional to sides

P Q

and

P R

and median

P M

of another

Δ

PQR. Show that

△ A B C \sim △ P Q R

Q. In

△ P Q R, s e g P M

is the median. Bisectors of

∠ P M Q

and

∠ P M R

intersect side

P Q

and side

P R

in points

X

and

Y

respectively, then prove that

X Y ∥ Q R

Q. PR is diagonal of a parallelogram PQRS. Show that

Δ

PQR

≅

Δ

RSP.

In the given figures, the sides AB and BC and the median AD of $Δ$ ABC are respectively equal to the sides PQ and QR and median PS of
$Δ$ PQR. Hence $Δ A B C$ and $Δ P Q R$ are right-angled triangles.

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

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In Δ PQR, seg PM is a median of ΔPQR. Bisectors of ∠PMQ and ∠PMR intersect side PQ and PR at X and Y respectively. Show that Δ PQR is similar to Δ PXY.

∠QMP+∠PMR=180∘L.pair∠PXY+∠QXY=180∘{L.P}∠PYX+∠RYX=180∘Sum of angle formed but 0 is 180∘1.e L.P {Axioro}

In $Δ$ PQR, seg PM is a median of $Δ$ PQR. Bisectors of $∠$ PMQ and $∠$ PMR intersect side PQ and PR at X and Y respectively. Show that $Δ$ PQR is similar to $Δ$ PXY.

$\begin{matrix} ∠ Q M P + ∠ P M R = 180^{\circ} L . p a i r ∠ P X Y + ∠ Q X Y = 180^{\circ} {L . P} ∠ P Y X + ∠ R Y X = 180^{\circ} \end{matrix}$
Sum of angle formed but 0 is $180^{\circ}$
1.e L.P {Axioro}