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Otheorem 7.3 A quadrileteral with diagonals other is bisecting parallelogram_ each Given:To be proved:ConclusionJustification71,72,#3, & congruence propertytri...

Question

Otheorem 7.3 A quadrileteral with diagonals other is bisecting parallelogram_ each Given:To be proved:ConclusionJustification71,72,#3, & congruence propertytriangle#7,#8,#9, & congruence propertytriangle#10.#I1_#6,#12, and definition of

Otheorem 7.3 A quadrileteral with diagonals other is bisecting parallelogram_ each Given: To be proved: Conclusion Justification 71,72,#3, & congruence property triangle #7,#8,#9, & congruence property triangle #10. #I1_ #6,#12, and definition of



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PROVING A THEOREM Prove the Parallelogram Diagonals Converse Theorem 7.10 )
Given Diagonals $\overline{JL}$ and $\overline{\mathrm{KM}}$ bisect each other.
Prove JKLM is a parallelogram.

Since the mid points are the same. This suggests that the diagonals bisect each other.

We know that a rhombus is a special quadrilateral because it's diagonals bisect each other at right angles. This divides the square into four concurrent right triangles. We also know that the concurrent angles, for example, triangle W V acts is equivalent to triangle. Why the X, which is equivalent to triangle W V C and triangle y v Z So we know that looking at the vert Osias, we can deduce that angle Z W acts equals angle. X y Z equals and then angle w z Why equals angle Y x w.

Question number 27. Yeah. It was given that there is a product where two diagonals are controlled to each other. Exactly one of the budget payers. Okay. Our budget. Yes. Are also Congress. They're the two triangles. But I just did this. So let us draw your data. So two sides are exactly congruent senators stolen this. So we see the rest of them an 80. And basically these two sides are congruent to each other. I was given that the triangles also. So the diagnosis. I'm going to put a CN videos of 100 to each other. There's this one E that approved two triangles form, sir. I just said this may be A B and C. D. Yes. It's hard to prove it. So where does do it? Art is given that ah S. E. Yes. I'm going to well be careful diagrams is given. Okay, protest. Let's try to start my child vision masters. They see this. I'm going to really for this girl also has given that Eddie it's going going to you see that is also given. Now I can say that cd is I'm going to city. This is a difficult super. Right then you can see that stronger. The sea is going going to strangle the C. D. This is yes as as as can take 123 all procedures. I'm going to each other. Okay so it starts to convert. You can see this is the first one. This angle is too so you can see angle one is coming going hungry too. Right? Because uh huh corresponding parcel Condoned 20 years younger. Right? The younger one. And to work I'm going there the side facing there under Thanks to being good. So I can see that the is converted to see. Right? So this is where the five was 200 congress non pregnancy during it D. C. You guys resent us. Right. Uh huh. Thank you guys be easy for to see. No, this is one this is one component for one another questions. Let's go to the next one. Let's go to number eight. And you can see that you can see a B minus R. And D. Is congruent to sc sc You can see the and see along. Great. You see and the media and great. So there are different also become good. Right? So this is the substructure in principle. It's obstruction principle. When one convert segments has obstructed from other Congress, 100 multi segments are congruent the decision. Nothing but And yeah, convert into. Mhm Great. We can say with conviction no longer. Mhm. Mhm. You know, try system. Right. Is a second language. Hands. Turn that. Mm hmm. To be me and longer. I do. Uh huh. Group. Thank you.

Let us calculate the slope of h l first. Why? To minus y one over X two minus X one is equivalent to zero. The soap of J K. Why? To minus y one over. Acts to minus X one is also equivalent is here. Now we know a challenge. A cab, the same slope. Therefore Rachel is parallel to J. K. Remember, parallel lines have the same slope. Okay. The slope of H J. The soul of a J. We're doing the same thing. Why? To minus y one over x two minus x one. We end up with negative seven over three for the soap of lk. Why? To minus y one over x two months x one, we end up with seven over three. As you can see, it's Jane. Lk do not have the same slope there for h j is not parallel to lk. So now looking at H. J talking into the distance formula, we have four minus one swear plus to minus nine squared, which is equivalent to the square root of 58. Now we have for lk five months, eh squared plus two minus nine squared which is equivalent to the square root of 58. Okay, we know because A J is equivalent to okay, H J is congruent to lk. Therefore, M and P Q is indeed nice. Sausages, trapezoid. We know that M. N P Q has exactly one pair of parallel sides of the legs or congrats.


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