Question

The triangle above is isosceles and b> a. Which of the following must be FALSE?

Answer 1

If the triangle is isosceles and b is greater than a then,

(c) AC = BC is false.

An isosceles triangle in geometry is one with at least two equal-length sides. It can be defined as having exactly two equal-length sides or as having at least two equal-length sides, with the equilateral triangle being an exception to the second definition.

The triangle is an isosceles triangle and angle b is greater than angle b.

For option (A),

AB = BC, therefore a = c which is possible.

For option (B),

AB = AC, therefore b = c which is also possible.

For option (C),

AC = BC, therefore a =b.

But we have b > a. Hence AB  = BC is false.

For option (D),

a = c, therefore AB = BC which is possible according to the properties of an isosceles triangle.

Option (C) is false.

Learn more about isosceles triangle here:

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The complete question is mentioned below:

Figure not drawn to scale. The triangle above is isosceles and b > a. Which of the following must be FALSE?

A) AB = BC

B) AB = AC

C) AC = BC

D) a = c