maths

State the congruency of following pairs of triangles.

In $ΔABC$ and $ΔPQR$, $BC=QR,$ $∠A=90_{∘},∠C=∠R=40_{∘}$ and $∠Q=50_{∘}$.

$∠A=90_{o}$, $∠C=40_{o}$

Sum of all angles of a triangle $=180_{o}$

$∠A+∠B+∠C=180_{o}$

$90_{o}+∠B+40_{o}=180_{o}$

$∴∠B=50_{∘}$

Now, In $△ABC$ and $△PQR$

$BC=QR$ (Given)

$∠C=∠R=40_{o}$ (Given)

$∠B=∠Q=50_{o}$

Thus, $△ABC≅△PQR$ (ASA rule)

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$(i)D$ is the mid-point of $AC$

$(ii)MD⊥AC$

$(iii)CM=MA=21 AB$

$(i)D$ is the mid-point of $AC$

$(ii)MD⊥AC$

$(iii)CM=MA=21 AB$

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Is $BP$>$PQ$ .

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(i) $ΔAPD≡ΔCQB$

(ii) AP=CQ

(iii) $ΔAQB≡ΔCPD$

(IV) AQ=CP

(V) APCQ is a parallelogram

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$(i)$ the triangle are congruent.

$(ii)$ the triangle are not congruent.

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$∠BOP=3∠COP$

State whether the above statement is true or false.

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i) $AM=AN$

ii) $ΔAMC≅ΔANB$

iii) $BN=CM$

iv) $ΔBMC≅ΔCNB$

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