Does anyone know what b is?

b = 17

Step-by-step explanation: The figure shows a triangle which upon closer observation is actually two triangles placed one inside the other. We have triangle QTR (the larger one) and triangle PTS (the smaller one).

The line PS is parallel to line QR, so in effect what we have here are two similar triangles. The ratios of similarity can be derived as

Line QT/line TR = line PT/line TS OR

Line QT/line QR = line PT/line PS.

With these ratios in mind we can now write the following expressions from the similar triangles;

QT = 2b + (2b - 17) and

TR = 16 + 8

TR = 24

Hence,

2b/16 = 2b + (2b - 17)/24

(That is, PT/TS = QT/TR)

2b/16 = (4b - 17)/24

By cross multiplication we now have,

2b(24) = 16(4b - 17)

By expanding the brackets we now have

48b = 64b - 272

By collecting like terms, 64b now moves to the left side of the equation and becomes negative

48b - 64b = -272

-16b = -272

Divide both sides of the equation by -16

b = 17

**Note** A negative number divided by another negative number yields a positive answer.

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

c

step-by-step explanation: