Question

In a triangle ABC,AC=BC. Write an angle equal to B​

Answer 1

Answer:

Step-by-step explanation:

I assume the axioms of Euclidean Geometry, and provide a sloppy proof without showing all steps rigorously, defending all my statements, or providing the diagrams that would make them clearer.

Since D is on BC, We have these five cases:

C is between D and B

D is congruent to C

D is between C and B

D is congruent to B

B is between D and C

I’ll start with 2 and 4:

Case 2) If D is congruent C, then the length of DC = 0. Since the length of DC = the length of AB, then the length of AB is 0. Therefore AB cannot be the edge of a triangle, ruling out this case.

Case 4) In this scenario, we return to the problem statement and replace D with B. We quickly notice that not only does the length of AC = the length of BC, but also the length of AB = the length of BC.

Therefore, the lengths of AB, BC, and AC are all equal, so the triangle is equilateral, and the measure of angle C is 60 degrees.

Cases 1, 3, and 5)