Congruence of Arcs

Q. In the given figure, chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD

Q. In the given figure, ∆QRS is an equilateral triangle. Prove that,
(1) arc RS ≅ arc QS ≅ arc QR
(2) m(arc QRS) = 240°.

Q. In the given figure, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof.

Q.

In the given figure, chords $AB=CD,\angle COD={60}^{\circ }$ and $\angle AOD={170}^{\circ }$.

Find the value of $\angle BOC$.

Q. The measure of minor arc of the circle is ${140}^o$. Find the measure of major arc.

1. ${220}^o$
2. ${310}^o$
3. ${350}^o$
4. None of these

Q. The two arcs, arc AB and arc EF are congruent.

1. False
2. True

Q. A, B, C are any points on the circle with centre O. m(arc BC)=140${}^{\circ }$ and m(arc AB)=100${}^{\circ }$. Then m(arc ABC) = .

1. 40${}^{\circ }$
2. 260${}^{\circ }$
3. 220${}^{\circ }$
4. 240${}^{\circ }$

Q. $\angle AMB$ is

1. ${220}^o$
2. ${80}^o$
3. ${110}^o$
4. ${170}^o$

Q. A, B, C are any points on the circle with centre O. m(arc BC)=120${}^{\circ }$ and m(arc AB)=130${}^{\circ }.$
Then,

1. ${250}^{\circ }$
2. ${110}^{\circ }$
3. ${230}^{\circ }$
4. ${240}^{\circ }$

Q. If arc(AC) and arc(DE) are congruent and AC = 4 cm, then DE = _____.

1. 2 cm
2. 4 cm
3. 6 cm
4. 5 cm

Q. The sector corresponding to the arc congruent to arc(AB) is

1. 
2. 
3. 
4. 

Q. Two arcs are congruent if their measures and radii are equal.

1. False
2. True