Advertisements
Advertisements
प्रश्न
In the following figure, OA = OC and AB = BC.
Prove that:
(i) ∠AOB = 90o
(ii) ΔAOD ≅ ΔCOD
(iii) AD = CD
Advertisements
उत्तर
Given:
In the figure, OA=OC, AB =BC
We need to prove that,
AOB = 90°
(i) In ΔABO and ΔCBO,
AB = BC ...[given ]
AO = CO ...[ given ]
OB = OB ...[ common ]
∴By Side-Side-Side criterion of congruence, we have
ΔABO ≅ ΔCBO
The corresponding parts of the congruent triangles are congruent.
∴∠ABO = ∠CBO ...[c. p.c.t. ]
⇒ ∠ABD = ∠CBD
and ∠AOB = ∠COB ...[c. p.c t ]
We have
∠AOB + ∠COB = 180° .....[ linear pair ]
⇒ ∠AOB = ∠ COB= 90° and AC ⊥ BD
(ii) In ΔAOD and ΔCOD,
OD = OD ...[ common ]
∠AOD = ∠COD ...[ each=90° ]
AO = CO ...[ given]
∴By Side-Angel-Side criterion of congruence, we have
ΔAOD ≅ ΔCOD
(iii) The corresponding parts of the congruent
triangles are congruent.
∴AD = CD ...[c. p.c t ]
Hence proved.
APPEARS IN
संबंधित प्रश्न
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to ∠E
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(DF)`
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: (i) AM = AN (ii) ΔAMC ≅ ΔANB
The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that:
In the given figure, prove that:
(i) ∆ ACB ≅ ∆ ECD
(ii) AB = ED
In the given figure P is a midpoint of chord AB of the circle O. prove that OP ^ AB.
Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.
It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR? Why?
