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Trapezoids and Kites HW - Printable Mathematics Worksheets - Wayground

Trapezoids and Kites HW

21 questions

10th - 10th Grade

Mathematics

Trapezoids and Kites HW is a Grade 10 mathematics worksheet that develops students’ ability to identify parts and apply geometric properties of trapezoids and kites. Through 21 items—17 open-ended questions and 4 fill-in-the-blank questions—students name bases and legs, identify congruent angles and segments, determine unknown angle measures, and solve algebraic angle relationships in trapezoids. Several items require students to show their work and use given relationships to find all four angles. The worksheet also includes multi-step kite problems involving side lengths, diagonals, right-triangle calculations, simplest radical form, decimal rounding, and angle measures. It is designed for homework, independent practice, or a geometry review that checks both vocabulary and problem-solving. This free printable worksheet includes a complete answer key, helping teachers quickly verify students’ work on angle relationships, segment measures, and calculations involving trapezoid midsegments and kite diagonals.

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Worksheets

Trapezoids and Kites HW

Total questions: 21

Name
Class
Date
1.

Name the bases of trapezoid PQRS.

4 lines
2.

Name the legs of trapezoid PQRS.

4 lines
3.

Name two pairs of congruent angles.

4 lines
4.

Name a pair of congruent segments.

4 lines
5.

If AX = 4, then CD = (a)   .

6.

If m∠ABC = 110°, then m∠BAD = (a)   .

7.

If m∠BAD = 65°, then m∠CDA = (a)   .

8.

If m∠DCB = 105°, then m∠DAB = (a)   .

9.

Trapezoid ABCD. Show all work. EF is a midsegment. m∠B is three times m∠C. Find m∠B and m∠C. (Hint: Let m∠C = x°).

4 lines
10.

If m∠A = (2x)°, m∠D = (x - 12)°, m∠B = y° and m∠C = (y - 70)°, find measures of all four angles.

4 lines
11.

Refer to kite PQRS with PQ = QR = 10, PR = 16, RS = 12. TR = _____.

4 lines
12.

Refer to kite PQRS with PQ = QR = 10, PR = 16, RS = 12. QT = _____.

4 lines
13.

Refer to kite PQRS with PQ = QR = 10, PR = 16, RS = 12. TS = _____ (Simplest Radical form).

4 lines
14.

Refer to kite PQRS with PQ = QR = 10, PR = 16, RS = 12. QS = _____ (rounded to nearest hundredth).

4 lines
15.

If m∠QRT = 40°, then m∠PQR = _____.

4 lines
16.

If m∠PSR = 30°, then m∠TRS = _____.

4 lines
17.

Refer to kite WXYZ. m∠VYZ = _____.

4 lines
18.

Refer to kite WXYZ. m∠XWZ = _____.

4 lines
19.

Refer to kite WXYZ. m∠VXY = _____.

4 lines
20.

Refer to kite WXYZ. m∠WXY = _____.

4 lines
21.

Refer to kite WXYZ. m∠WZY = _____.

4 lines
Answer Key

Trapezoids and Kites HW

Total questions: 21

1.
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2.
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3.
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4.
n/a
5.
8
6.
70°
7.
65°
8.
75°
9.
n/a
10.
n/a
11.
n/a
12.
n/a
13.
n/a
14.
n/a
15.
n/a
16.
n/a
17.
n/a
18.
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19.
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20.
n/a
21.
n/a

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FAQs

What does the Trapezoids and Kites HW worksheet cover?

This Grade 10 worksheet uses open-ended and fill-in-the-blank questions to assess trapezoid and kite properties. Students identify trapezoid bases and legs, recognize congruent angles and segments, solve unknown angles using geometric relationships and algebra, and calculate kite segment lengths with right-triangle reasoning, radical notation, and rounding.

How can I use this worksheet to teach trapezoid and kite properties?

Begin by having students annotate the trapezoid diagrams, labeling bases, legs, congruent parts, and relevant angles before attempting the numerical items. Then model one angle problem using an equation, such as relating two angles whose measures are connected, and one kite problem by separating the figure into right triangles. Use the show-your-work questions to discuss why each relationship or calculation is valid.

What mistakes should I watch for on this trapezoids and kites worksheet?

Students may confuse a trapezoid’s bases with its legs or identify congruent parts without matching the labels correctly. In the angle problems, watch for skipped algebra, incorrect use of angle relationships, and failure to account for the expressions involving x and y. In the kite problems, students may choose the wrong right-triangle legs, leave a radical unsimplified, or round before reaching the final step.

How do I assign and grade this Trapezoids and Kites HW worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for checking the 21 responses. For printable submissions, scan student work with the Wayground for Teachers app to help grade the open-ended trapezoid and kite calculations as well as the fill-in-the-blank items.

How can I differentiate this worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the diagram-labeling, angle-equation, and multi-step kite items easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while preserving its trapezoid and kite practice format.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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