Let ABCD be a parallelogram- Let AP- CQ be the perp from A and C on its diagonal BD- Which of the following is true-CQ-PDAP-BQAP-CQPD-QB

Question

Toppr Admin · Accepted Answer

From -x394-APD and -x394-BQCAD - BC-Since- ABCD is a -x2223-x2223- gm -x2234-AD-BC- -x2220-ADP-x2220-CBQ-Since- AD -x2223-x2223- BC and and BD is transversal-lt-br-gt-lt-br-gt-x2220-APD-x2220-CQB -each 90-x2218-x394-APD-x2245-x394-BQC -By AAS rule-AP-CQ

Let ABCD be a parallelogram. Let AP, CQ be the $⊥$ from A and C on its diagonal BD. Which of the following is true.
$C Q = P D$
$A P = B Q$
$A P = C Q$
$P D = Q B$

From $Δ A P D$ and $Δ B Q C$
AD $=$ BC
(Since, ABCD is a $∣ ∣$ gm $∴ A D = B C$ )
$∠ A D P = ∠ C B Q$
[Since, AD $∣ ∣$ BC and and BD is transversal]<br><br> $∠ A P D = ∠ C Q B$ [each $90^{\circ}$ ]
$Δ A P D ≅ Δ B Q C$ [By AAS rule]
$A P = C Q$

Let ABCD be a parallelogram. Let AP, CQ be the ⊥ from A and C on its diagonal BD. Which of the following is true.CQ=PDAP=BQAP=CQPD=QB

From ΔAPD and ΔBQCAD = BC(Since, ABCD is a ∣∣ gm ∴AD=BC) ∠ADP=∠CBQ[Since, AD ∣∣ BC and and BD is transversal]<br><br>∠APD=∠CQB [each 90∘]ΔAPD≅ΔBQC [By AAS rule]AP=CQ

Let ABCD be a parallelogram. Let AP, CQ be the $⊥$ from A and C on its diagonal BD. Which of the following is true.
$C Q = P D$
$A P = B Q$
$A P = C Q$
$P D = Q B$

From $Δ A P D$ and $Δ B Q C$
AD $=$ BC
(Since, ABCD is a $∣ ∣$ gm $∴ A D = B C$ )
$∠ A D P = ∠ C B Q$
[Since, AD $∣ ∣$ BC and and BD is transversal]<br><br> $∠ A P D = ∠ C Q B$ [each $90^{\circ}$ ]
$Δ A P D ≅ Δ B Q C$ [By AAS rule]
$A P = C Q$