# Write a two-column proof in exercises 11 and 12 development

And this side is parallel to that side.

RP is parallel to TA. Because there is a lot of information to follow, we have a new illustration of this problem below that shows congruent sides and angles.

### Write a two-column proof in exercises 11 and 12 development

That's not true. If it looks something like this. And they say, what's the reason that you could give. That's right there. And I can make the argument, but basically we know that RP, since this is an isosceles trapezoid, you could imagine kind of continuing a triangle and making an isosceles triangle here. The other example I can think of is if they're the same line. RP is congruent to TA.

For example, this is a parallelogram. Anyway, that's going to waste your time.

So I think what they say when they say an isosceles trapezoid, they are essentially saying that this side, it's a trapezoid, so that's going to be equal to that.

It says, use the proof to answer the question below.

## Segment and angle proofs

Kind of like an isosceles triangle. Let me see how well I can do this. Inequalities of a Triangle Recall that an inequality is a mathematical expression about the relative size or order of two objects. They're saying that this side is equal to that side. And I don't want the other two to be parallel. A Making Mathematics teacher, in the midst of doing research with colleagues, shared his feelings about proof: In practice, proofs may involve diagrams that clarify, words that narrate and explain, symbolic statements, or even a computer program as was the case for the Four Color Theorem MacTutor. And I can make the argument, but basically we know that RP, since this is an isosceles trapezoid, you could imagine kind of continuing a triangle and making an isosceles triangle here. If this was the trapezoid. Statement two, angle 1 is congruent to angle 2, angle 3 is congruent to angle 4. That's the definition of parallel lines. Well, what if they are parallel? And say oh well choice C looks pretty good. So both of these lines, this is going to be equal to this. So this is T R A P is a trapezoid.

Proof 6. They're saying that this side is equal to that side.

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