given: OR congruent to OP, OE bisects <ROP. Prove: <3 congruent to <4

Question

its a triangle.

O is at the top

R is on the bottom left

E is on the bottom middle

P is on the bottom right

the triangle has a line in the middle and on the left it has #1 top left, #3 bottom left and on the right it has #2 on the top right and #4 on the bottom right

Answer 1

IF OR is congruent to OP, then the triangle is isosceles and angle 3 is congruent to angle 4 by definition. But to prove it:

OR ≅ OP Given

OE bisects ∠ROP Given

∠1 ≅ ∠2 Definition of angle bisector

OE ≅ OE Reflexive Property

triangle ROE ≅ triangle POE SAS

∠3 ≅ ∠4 CPCTC