# Write a conjecture about the midsegment of a trapezoid

Student Web Links Properties of the Midsegment of a Trapezoid The midsegment of a trapezoid connects the midpoints of the two nonparallel sides of the trapezoid. Construct viable arguments and critique the reasoning of others. While many of these angle relationships are review for students, students must use a new strategy to solve this problem: I have found that the most effective way to debrief this Warm-up is not to have a student present the answers—this takes far too long—but rather to simply post the answers for students to check and to ask students to share out about which angles they thought were the most challenging to find and the strategy they used to find them.

WU Ordered Angle Chase. Kite and Trapezoid Properties 15 minutes Since we have discussed kite and trapezoid properties in the past, this activity provides time for my students to refresh their understanding of the properties.

I plan to pass out tracing paper and ask my students to take out compasses and straightedges so that they can "re-investigate" some of the properties about the angles and the diagonals of these polygons, as needed.

I circulate the room while students are re-investigating and recording the kite and trapezoid properties. When most groups seems to be finishing, I debrief the properties with the whole class. Kites and Trapezoids Notes KEY Polygon Progression 20 minutes In Task 1 of Polygon Progressiongroups of students use construction tools and tracing paper to discover something new about the midsegments of triangles and trapezoids. Like other group investigations in our class, each member of the group investigates their own special case of triangle and trapezoid midsegments and then compares their results with the group so they can conjecture about midsegments.

When every member of the group knows and can defend their conjecture, they check in with me to share their ideas and to justify their reasoning MP3.13 Which is a counterexample to the conjecture that the product of 3 and any integer is a multiple of 6?

20 Write a congruence statement for the following triangles.

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38 Find the length of the midsegment of the trapezoid shown. 39 MNPQ is a kite. Find. 40 Find x. Line DE is the midsegment of triangle ABC.

It connects the two midpoints of the two sides of a triangle. It is equal to one half the length of the base. It is parallel to the base. It forms a smaller triangle with all the same angle measures, one-half the perimeter, and one-fourth the area of the original triangle.

If one base of the trapezoid shrinks to a point, the trapezoid collapses into a triangle, the midsegment of the trapezoid becomes a midsegment of the triangle, and the Trapezoid Midsegment Conjecture becomes the Triangle Midsegment Conjecture.

In the sketch, you saw trapezoid . A trapezoid midsegment connects the midpoints of the two congruent sides of the trapezoid, and is parallel to the pair of parallel sides.

## Warm-Up: The Ordered Angle Chase

The length of the midsegment is the sum of the two bases divided by 2. Remember that the bases of a trapezoid are the two parallel sides.

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Prove that E and F lie on the midsegment of the trapezoid If AB=10 and Stack Exchange Network Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Open-Ended Draw a triangle and all of its midsegments. Make a conjecture about what appears to be true about the four triangles that result. What postulates could be used to prove the conjecture? Coordinate Geometry Th e coordinates of the vertices of a triangle are K(2, 3), L(22, 21), and M(5, 1).

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