Advertisements
Advertisements
प्रश्न
In Fig. 10.99, AD ⊥ CD and CB ⊥. CD. If AQ = BP and DP = CQ, prove that ∠DAQ = ∠CBP.
Advertisements
उत्तर
Given that, in the figure AD ⊥ CD and CB ⊥ CD and AQ = BP,DP =CQ
We have to prove that ∠DAQ=∠CBP
Given that DP= QC
Add PQ on both sides
Given that DP=QC
Add PQ on both sides
⇒ DP+PQ=PQ+QC
⇒ DQ=PC ................(1)
Now, consider triangle DAQ and CBP,
We have
∠ADQ=∠BCP=90° [given]
AQ=BP [given]
And DQ=PC [given]
So, by RHS congruence criterion, we have ΔDAQ≅ΔCBP
Now,
∠DAQ=∠CBP [ ∵Corresponding parts of congruent triangles are equal]
∴ Hence proved
APPEARS IN
संबंधित प्रश्न
You want to show that ΔART ≅ ΔPEN,
If you have to use SSS criterion, then you need to show
1) AR =
2) RT =
3) AT =
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
In the given figure, prove that:
CD + DA + AB + BC > 2AC
The following figure shows a circle with center O.
If OP is perpendicular to AB, prove that AP = BP.
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD.
Prove that :
(i) ΔABD and ΔECD are congruent.
(ii) AB = CE.
(iii) AB is parallel to EC
In the given figure: AB//FD, AC//GE and BD = CE;
prove that:
- BG = DF
- CF = EG
In the adjoining figure, QX and RX are the bisectors of the angles Q and R respectively of the triangle PQR.
If XS ⊥ QR and XT ⊥ PQ;
Prove that:
- ΔXTQ ≅ ΔXSQ.
- PX bisects angle P.
In the figure, given below, triangle ABC is right-angled at B. ABPQ and ACRS are squares. 
Prove that:
(i) ΔACQ and ΔASB are congruent.
(ii) CQ = BS.
In the following figure, OA = OC and AB = BC.
Prove that: ΔAOD≅ ΔCOD
