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Trapezoids: Midsegments, Angles & Diagonals — Easy Worksheet 1
Grade 10 · Whoobee Name: ____________________ Date: __________
In each trapezoid ABCD, AB ∥ DC, with AB on top. When M and N are shown, they are the midpoints of the legs AD and BC, so MN is the midsegment.
How to solve
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Example
MN is the midsegment of trapezoid ABCD. AB = 10 and DC = 12. Find MN.
Answer: 11
Not quite. The answer is
💡 The midsegment is the average of the bases: MN = AB + DC2 = 9 + 192 = 282 = 14. So MN = 14.
✓ Correct!
Not quite. The answer is
💡 The midsegment is the average of the bases: MN = AB + DC2 = 9 + 192 = 282 = 14. So MN = 14.
💡 How to solve: Trapezoids: Midsegments, Angles & Diagonals
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Try a similar one
MN is the midsegment of trapezoid ABCD. AB = 7 and DC = 17. Find MN.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 ∠A and ∠D are on the same leg between the parallel bases, so they add up to 180°: m∠A = 180° − 77° = 103°. The top base angles are equal too, so m∠B = m∠A = 103°.
✓ Correct!
Not quite. The answer is
💡 ∠A and ∠D are on the same leg between the parallel bases, so they add up to 180°: m∠A = 180° − 77° = 103°. The top base angles are equal too, so m∠B = m∠A = 103°.
💡 How to solve: Trapezoids: Midsegments, Angles & Diagonals
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Try a similar one
MN is the midsegment of trapezoid ABCD. AB = 5 and DC = 11. Find MN.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 MN = AB + DC2, so AB + DC = 2 · MN = 2 · 10 = 20. Subtract AB: DC = 20 − 8 = 12. So DC = 12.
✓ Correct!
Not quite. The answer is
💡 MN = AB + DC2, so AB + DC = 2 · MN = 2 · 10 = 20. Subtract AB: DC = 20 − 8 = 12. So DC = 12.
💡 How to solve: Trapezoids: Midsegments, Angles & Diagonals
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Try a similar one
MN is the midsegment of trapezoid ABCD. AB = 9 and DC = 15. Find MN.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The legs are equal, so BC = AD = 12. Perimeter = AB + BC + DC + AD = 6 + 12 + 8 + 12 = 38.
✓ Correct!
Not quite. The answer is
💡 The legs are equal, so BC = AD = 12. Perimeter = AB + BC + DC + AD = 6 + 12 + 8 + 12 = 38.
💡 How to solve: Trapezoids: Midsegments, Angles & Diagonals
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Try a similar one
MN is the midsegment of trapezoid ABCD. AB = 5 and DC = 11. Find MN.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The midsegment is the average of the bases: MN = AB + DC2 = 4 + 142 = 182 = 9. So MN = 9.
✓ Correct!
Not quite. The answer is
💡 The midsegment is the average of the bases: MN = AB + DC2 = 4 + 142 = 182 = 9. So MN = 9.
💡 How to solve: Trapezoids: Midsegments, Angles & Diagonals
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Try a similar one
MN is the midsegment of trapezoid ABCD. AB = 7 and DC = 17. Find MN.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 AB ∥ DC, so ∠A and ∠D, on the same leg, are same-side interior angles and add up to 180°. m∠A = 180° − 53° = 127°.
✓ Correct!
Not quite. The answer is
💡 AB ∥ DC, so ∠A and ∠D, on the same leg, are same-side interior angles and add up to 180°. m∠A = 180° − 53° = 127°.
💡 How to solve: Trapezoids: Midsegments, Angles & Diagonals
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Try a similar one
MN is the midsegment of trapezoid ABCD. AB = 10 and DC = 12. Find MN.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The diagonals of an isosceles trapezoid are equal, so AC = BD = 21.
✓ Correct!
Not quite. The answer is
💡 The diagonals of an isosceles trapezoid are equal, so AC = BD = 21.
💡 How to solve: Trapezoids: Midsegments, Angles & Diagonals
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Try a similar one
MN is the midsegment of trapezoid ABCD. AB = 6 and DC = 8. Find MN.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 MN = AB + DC2, so AB + DC = 2 · MN = 2 · 13 = 26. Subtract AB: DC = 26 − 10 = 16. So DC = 16.
✓ Correct!
Not quite. The answer is
💡 MN = AB + DC2, so AB + DC = 2 · MN = 2 · 13 = 26. Subtract AB: DC = 26 − 10 = 16. So DC = 16.
💡 How to solve: Trapezoids: Midsegments, Angles & Diagonals
The midsegment of a trapezoid joins the midpoints of the two legs. It is parallel to the bases and its length is the average of the bases: MN = AB + DC2. The two angles on the same leg add to 180°: m∠A + m∠D = 180°. In an isosceles trapezoid the legs are equal, the base angles are equal in pairs (∠D = ∠C and ∠A = ∠B), and the diagonals are equal (AC = BD).
Try a similar one
MN is the midsegment of trapezoid ABCD. AB = 11 and DC = 21. Find MN.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Trapezoids: Midsegments, Angles & Diagonals — Easy Worksheet 1
In each trapezoid ABCD, AB ∥ DC, with AB on top. When M and N are shown, they are the midpoints of the legs AD and BC, so MN is the midsegment.