three night guard A, B and C blow their whistles at intervals of 8, 15 and 18 mins respectively, if they blow at 11.00pm, when next are they expected to blow together

5:00 AM

Solution:

we will have to find the lowest common multiple of 8 , 5 and 18.

Since they blow their whistles once every 8/5/18 minutes.. you can imagine it as the multiplication table for these numbers. The number on which all three overlap,  is the LCM and hence the amount of time after they will blow their whistles together.

The LCM is 360

therefore, the guards will blow their whistles together 360 minutes after 11:00pm

360 minutes  = 6 hours

6 hours after 11:   5:00AM

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc