The word trinity means a unity of 3 parts. The Trinity River in Texas gets its name from the fact that it is formed from 3 distinct sources.
Jn 1:1-14
JOHN 1 In the beginning was the Word, and the Word was with God, and the Word was God.
2 The same was in the beginning with God.
3 All things were made by him; and without him was not any thing made that was made.
4 In him was life; and the life was the light of men.
5 And the light shineth in darkness; and the darkness comprehended it not.
6 There was a man sent from God, whose name was John.
7 The same came for a witness, to bear witness of the Light, that all men through him might believe.
8 He was not that Light, but was sent to bear witness of that Light.
9 That was the true Light, which lighteth every man that cometh into the world.
10 He was in the world, and the world was made by him, and the world knew him not.
11 He came unto his own, and his own received him not.
12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
13 Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
KJV
Here we clearly see two distinct members of the Godhead.
Jn 16:7-15
7 Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.
8 And when he is come, he will reprove the world of sin, and of righteousness, and of judgment:
9 Of sin, because they believe not on me;
10 Of righteousness, because I go to my Father, and ye see me no more;
11 Of judgment, because the prince of this world is judged.
12 I have yet many things to say unto you, but ye cannot bear them now.
13 Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
14 He shall glorify me: for he shall receive of mine, and shall shew it unto you.
15 All things that the Father hath are mine: therefore said I, that he shall take of mine, and shall shew it unto you.
KJV
Here we see that the Holy Spirit has all the attributes of personhood.
Ge 1:1-2
GENESIS 1 In the beginning God created the Heaven and the earth.
2 And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
KJV
Here we see that the Holy Spirit is of God A person of God is a member of the Godhead by definition.
This is my basis for belief in a Trinity.
Jn 1:1-14
JOHN 1 In the beginning was the Word, and the Word was with God, and the Word was God.
2 The same was in the beginning with God.
3 All things were made by him; and without him was not any thing made that was made.
4 In him was life; and the life was the light of men.
5 And the light shineth in darkness; and the darkness comprehended it not.
6 There was a man sent from God, whose name was John.
7 The same came for a witness, to bear witness of the Light, that all men through him might believe.
8 He was not that Light, but was sent to bear witness of that Light.
9 That was the true Light, which lighteth every man that cometh into the world.
10 He was in the world, and the world was made by him, and the world knew him not.
11 He came unto his own, and his own received him not.
12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
13 Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
KJV
Here we clearly see two distinct members of the Godhead.
Jn 16:7-15
7 Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you.
8 And when he is come, he will reprove the world of sin, and of righteousness, and of judgment:
9 Of sin, because they believe not on me;
10 Of righteousness, because I go to my Father, and ye see me no more;
11 Of judgment, because the prince of this world is judged.
12 I have yet many things to say unto you, but ye cannot bear them now.
13 Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
14 He shall glorify me: for he shall receive of mine, and shall shew it unto you.
15 All things that the Father hath are mine: therefore said I, that he shall take of mine, and shall shew it unto you.
KJV
Here we see that the Holy Spirit has all the attributes of personhood.
Ge 1:1-2
GENESIS 1 In the beginning God created the Heaven and the earth.
2 And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
KJV
Here we see that the Holy Spirit is of God A person of God is a member of the Godhead by definition.
This is my basis for belief in a Trinity.