Question

Can you conclude that angle AB = angle BC? yes no

Answer 1

Answer: 1)Yes 2)Yes 3)No 4)Yes 5)Yes.

Step-by-step explanation:

Figure 1: In triangle ABC, AB=BC=6 given.As the measures are same we can say AB=BC.

Figure 2:Lines AC and BD meet at 90 degrees.BD is diameter of the circle .A perpendicular dropped from centre bisects the chord so AC is bisected by BD.The two triangles formed ABE and CEB  will be congruent by SAS congruence property.So by CPCTC we can say AB=BC.( see figure)

Figure 3: There is not enough information to prove AB and BC are equal.

Figure 4:AB and BC are making same angle 120 degrees at centre and as equal chords make equal angle at centre so we can say AB=BC.

Figure 5:The distance of chords AB and BC are same that is 2 units from the centre ,equal chords are equidistance from centre so AB=BC.

Answer 2

1) Yes 2 flat angles
2 yes 2 90° angles
3) no AB = CD and BC = AD
4) yes 120°
5 yes 2 flat angles