Question

ABCD is a parallelogram and AP and CQ are perpendiculars
from vertices A and C to diagonal BD.
If CQ = 4cm, BC= 5cm,PQ= 5cm, then BD will be


tell me the ans pls​

Answer 1

Answer:

In △APB and △CQD,

∠APB=∠CQD (Each 90 degree)

AB=CD (Opposite sides of parallelogram ABCD)

∠ABP=∠CDQ (Alternate interior angles for AB∥CD)

∴△APB≅△CQD (By AAS congruency)

∴AP=CQ by CPCT

Hence proved.

Hope it's help ☺️

Answer 2

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$\sf\underbrace{Correct\: Question: }$

• ABCD is a parallelogram and AP and CQ are perpendiculars From Vertices A and C on diagonal BD show that△APB ≈ △CQD.

$\sf\underline\red{Given: }$

• ABCD is parallelogram with AP ⊥ BD & CQ ⊥ BD

$\sf\underline\purple{To\:prove:}$

• △APB ≈ △CQD

$\sf\underline\orange{Solution:}$

Now,

• $⟹$$\sf{AB\: || \:DC \:and\: transversal \:BD.}$

• $\sf{⟹\:∠ABP\: = \:∠CDQ,\: (Alternate\: Angles)...(1)}$

• $⟹$$\sf{In\:△APB \:and\: △CQD,}$

• $⟹$$\sf{∠APB \:= \:∠CQD}$

• $⟹$$\sf{∠ABP\: = \:∠CDQ}$

• $⟹$$\sf{AB\: = \:CD}$

$\large{ \underline{ \boxed{ \textsf{∴\: △APB\: ≈ \:∠CQD}}}}$

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