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 `bar(DF)`
In a squared sheet, draw two triangles of equal areas such that
The triangles are congruent.
What can you say about their perimeters?
In the given figure, if AB = AC and ∠B = ∠C. Prove that BQ = CP.
Mark the correct alternative in each of the following:
If ABC ≅ ΔLKM, then side of ΔLKM equal to side AC of ΔABC is
If ΔABC ≅ ΔABC is isosceles with
Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
From the information shown in the figure,
In ΔABC and ΔPQR
∠ABC ≅ ∠PQR
seg BC ≅ seg QR
∠ACB ≅ ∠PRQ
∴ ΔABC ≅ ΔPQR ...`square` test
∴ ∠BAC ≅ `square` ...corresponding angles of congruent triangles.
`{:("seg AB" ≅ square),("and" square ≅ "seg PR"):}}` ...corresponding sides of congruent triangles
In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test?
Prove that:
- ∆ ABD ≅ ∆ ACD
- ∠B = ∠C
- ∠ADB = ∠ADC
- ∠ADB = 90°
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).
In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if ______.
