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True or False questions on linear pair and vertical angel questions

Please consider following questions in an attachment.  

In coming up with solution, I have drawn two pictures.  In the attachment where all four angles are right angles, all the questions will be TRUE because the angles in question will have same measure so they'll be congruent.  

I the other picture, some questions will be false and other will be true.  

Does this make sense that answer will depend on the picture drawn?
linear-pair-true-false.jpg
solution.bmp
Math / Science

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Paul Sauvé

8/22/2022 - Mon
naseeam

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This is high school geometry question.
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Paul Sauvé

Linear Pair of Angles

Vertical Angles

Since this is probably a homework question, we cannot solve the problem for you. But, you should be able to tell which of the statements 4 to 9 are always true and which are only true if the angles are right angles.

Remember that the sum of a Linear Pair of Angles will ALWAYS be 180 °.
naseeam

ASKER
This isn't homework problem.  I'm refreshing my geometry skills to help Geometry student prepare for a test.
Your help has saved me hundreds of hours of internet surfing.
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Paul Sauvé

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naseeam

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The perpendicular lines picture and other picture are not given in the problem.  I drew them to help me solve the problem.  It's just strange that both pictures satisfy pair of given angels.
And the answers to questions depend on the picture used.
The books answers match the non-perpendicular lines picture.  That make me wonder if other picture is even valid for this problem?
Paul Sauvé

From the definitions of linear and vertical angle pairs, both of the diagrams are valid. But I AM surprised that there is no diagram included with the statement of the problem! However, perpendicular intersecting lines are a special case, as is a the with a quadrilateral with parallel sides or with 2 right angles, or 4 right angles or 2 equal sides or 4 equal sides (Square, Rectangle, Rhombus, Trapezoid, etc.)!