Aidan H.

asked • 11/02/21

<2 is congruent to <1, <3 is congruent to <2. Are they talking about the transitive property or the substitution property?

Brenda D.

tutor
Did you mean the measure of angle 2 is congruent to the measure of angle 1? Do you have diagram, picture or link to what you are referring to. Hint you can also just look up the definitions as they apply to Geometry; Transitive Property is when two numbers, variables, or quantities are equal to the same thing (not necessarily each other right away as the given). You would also want to make sure you understand the meaning of Congruent.
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11/02/21

Aidan H.

No, I just meant angle 2 is congruent to angle 1, and angle 3 is congruent to angle 2! I don't know where I can find the diagram/picture/link, but I'll tell you the problem! The problem is thus: Given:r//s and <1 (congruent symbol)<3 Prove:p//q Here's How I Did It: Statement 1:r//s and <1 (congruent symbol)<3 Reason 1:Given Statement 2: <2 (congruent symbol)<1 Reason 2: corresponding angle postulate Statement 3: <3 (congruent symbol) <2 Reason 3: Transitive Property(this is where I'm concerned, because the middles don't match!) Statement 4: p//q Reason 4: Alternate interior angle converse Now the real question is "did I do it right?"
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11/02/21

Jon S.

You need to define where <3 is located in your diagram
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11/02/21

Aidan H.

Let me give you a descriptive version of the diagram since I don't have access to the image: a pair of parallel lines(r and s) are slanted vertically. Another pair of parallel lines(p and q) are laid out horizontally. At the bottom of line p(outside of lines r and s) is <3. At the top of line q(inside of lines r and s) is <2, and so is <1(but <1 is outside of lines r and s). Please draw the description provided and also solve the question. Thank you.
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11/02/21

1 Expert Answer

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Dan C. answered • 11/02/21

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It depends what you are trying to prove. But the way you're phrasing it makes it sound like the transitive property.

Given your statement, and according to the Transitive property, it follows that <3 is congruent to <1.


Using the Substitution property, and what you've given, you could substitute <1 for <2 if needed, and <3 for <2 if needed. Usually that means that you need to use it in conjunction with another step.


By the way, according to the Definition of Congruent Angles, you've also proved that you're looking at an equiangular triangle! Hope that helps.

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