How might you prove your observations from question 4 about the length of a midsegment using geometric theorems? Briefly outline an approach using what you know about midpoints, parallel lines, and congruent triangles. Use the figure you created in GeoGebra to guide you.

Question

07-10-2020
Mathematics

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How might you prove your observations from question 4 about the length of a midsegment using geometric theorems? Briefly outline an approach using what you know about midpoints, parallel lines, and congruent triangles. Use the figure you created in GeoGebra to guide you.

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rosalynros4 rosalynros4 · Answer 1 · 2020-10-08T09:52:12+02:00

Answer:

To prove the relationship about the length of a midsegment, I can use the properties of parallel lines and transversals. If I draw at least two midsegments, I see that they form congruent triangles within the original triangle, ∆ABC. I can prove the congruence of these triangles using triangle congruence criterion, and then use properties of congruent triangles and the Transitive Property to show that the length of the midsegment is half the length of the side it is parallel to.

Step-by-step explanation:

walker2021162 walker2021162 · Answer 2 · 2021-01-25T14:38:28+01:00

Answer:

To prove the relationship about the length of a midsegment, I can use the properties of parallel lines and transversals. If I draw at least two midsegments, I see that they form congruent triangles within the original triangle, ∆ABC. I can prove the congruence of these triangles using triangle congruence criterion, and then use properties of congruent triangles and the Transitive Property to show that the length of the midsegment is half the length of the side it is parallel to.

Step-by-step explanation:

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