How do I convince someone to trust the Bible?

First, we commend you for working to help your friend know Jesus, however, hearts will not be turned to faith in Jesus because we explain the origins of the pyramids or answer some other meaningless riddle. In truth, such questions are merely diversions on the part of an unbeliever to avoid participating in a real conversation about Jesus. Even your friend's supposition that "no one knows how Egyptians built the pyramids" is itself a red herring, since the construction of the pyramids is not a mystery today because Egyptologists can explain the methods men used to construct them. 

Such questions have no relevance to matters of God, Jesus, Heaven, sin and Hell. The only question that matters is, who is Jesus? Even if you can provide your friend with a satisfactory answer about the pyramids' origins and construction techniques, etc., he will undoubtedly raise another pointless question to keep the conversation away from Jesus. You should persist in talking about Jesus and what His death on the cross meant, and if that topic doesn't interest the person, then they were never truly interested in the first place.

Remember, saving faith requires a movement of the Holy Spirit in a person's heart, so the evangelist's role is not to argue someone into believing, for this is not even possible. We can't substitute our persuasion for the Spirit's power to bring faith. The Bible tells us that the word of God is foolishness to those who are perishing, so bringing a person to the point the understand and accept the word of God is a work that only God can do. We can quite simply participate in interesting conversation and answer questions, but, if the goal is evangelism, don't allow the other person to dictate the topic of conversation. 

We encourage you to listen to Lessons 10B through 10E in our Gospel of Matthew study to learn a biblical manner of reaching people with the Gospel.