Advertisements
Advertisements
प्रश्न
In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
Advertisements
उत्तर
Given:
In the figure, O is centre of the circle and PQ is a chord.
OM ⊥ PQ
To prove: PM = QM
Construction: Join Op and OQ
Proof:
In right triangles ΔOPM and ΔOQM,
OP = OQ ....[radii of the same circle]
OM = OM ....[common]
∴ By right angle-Hypotenuse-Side criterion of congruency,
ΔOPM ≅ΔOQM
The corresponding parts of the congruent triangles are congruent.
∴ PM = QM.
APPEARS IN
संबंधित प्रश्न
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to ∠E
If ΔABC ≅ ΔABC is isosceles with
Which of the following is not a criterion for congruence of triangles?
In the given figure, the measure of ∠B'A'C' is
In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC = 5 cm, then CD =
In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?
State, whether the pairs of triangles given in the following figures are congruent or not:
In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:
a. DABD andDECD are congruent.
b. AB = EC
c. AB is parallel to EC
In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.
ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.
Prove that
(i) BG = CH
(ii) AG = AH
