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🎯 Know Your Learning Goals
Hello, learner! In this session, you will meet two special quadrilaterals: the trapezoid and the kite. You will learn what makes each shape unique,and how to name its parts.
By the end of this lesson, I can:
define a trapezoid and a kite in my own words; and
identify the bases, legs, base angles, congruent sides, and diagonals of trapezoids and kites.
🧩 Explore and Build Understanding
Shape Detectives in Our Community
Look around you. Geometry is not limited to a textbook. Four-sided shapes can appear in terrace plots, woven baskets, windows, roofs, signs, and many other objects. Your first task is to observe before learning the formal names.
Study the images and think about these questions:
Which figures have four sides?
Do all opposite sides appear parallel?
Can you find a figure with exactly one pair of parallel sides?
Can you find a figure with two pairs of equal-length sides that meet at corners?
Sort the Shapes
Imagine that you have several quadrilateral cards. Sort them into groups. In the first group, place shapes with exactly one pair of parallel sides. In the second group, place shapes with two pairs of adjacent equal-length sides. A side is adjacent to another side when the two sides share a vertex. Put in another group those you believe do not belong to the first two groups.
As you sort, do not rely only on how a shape looks. Check the markings. Matching arrow marks show parallel sides. Matching tick marks show congruent sides.
What Is a Trapezoid?
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The word exactly matters. Previously, you learned that a quadrilateral with two pairs of parallel sides is a parallelogram and is different from trapezoid.
In trapezoid LOVE, LO ∥ EV. Let us name its parts:
Bases: LO and EV. These are the parallel sides.
Legs: LE and OV. These are the nonparallel sides.
Base angles on base LO: ∠L and ∠O.
Base angles on base EV: ∠E and ∠V.
Diagonals: LV and OE. A diagonal joins two nonadjacent vertices.
Notice that a base is not always at the bottom of a drawing. The parallel sides are the bases, regardless of the direction in which the figure is turned.
What Is a Kite?
A kite is a quadrilateral with two pairs of consecutive congruent sides. Consecutive sides share a vertex. In the definition used here, the opposite sides are not congruent.
In kite SELF:
SE ≅ EL. These equal sides meet at E.
SF ≅ FL. These equal sides meet at F.
SL and EF are the diagonals because they connect opposite vertices.
The matching tick marks, not the appearance alone, tell us which sides are congruent.
See How It Works
Example 1: Trapezoid PRSV has PR ∥ VS. Name its bases, legs, base angles, and diagonals.
First, find the sides marked parallel. PR and VS are parallel, so they are the bases. The remaining sides, PV and RS, are the legs. The base-angle pairs are ∠P and ∠R, then ∠V and ∠S. Finally, the diagonals connect opposite vertices, so they are PS and RV.
Example 2: In kite CORN, CN ≅ CO and NR ≅ OR. Name the congruent-side pairs and diagonals.
CN and CO form one pair because they meet at C. NR and OR form the other pair because they meet at R. The opposite vertex pairs are C and R, then N and O. Therefore, the diagonals are CR and NO.
Try It Yourself
Draw one trapezoid and one kite. Label all vertices. Then complete the following:
For the trapezoid, mark the parallel sides and name its bases, legs, base-angle pairs, and diagonals.
For the kite, mark the two pairs of consecutive congruent sides and name its diagonals.
Write one sentence explaining the most important difference between the two shapes.
📒 Check Your Understanding
Quick Check
Use trapezoid MATH with MA ∥ TH and kite KITE with KI ≅ KE and IT ≅ ET.
Name the bases of trapezoid MATH.
Name the legs of trapezoid MATH.
Name the two pairs of base angles of trapezoid MATH.
Name the two pairs of consecutive congruent sides of kite KITE.
Name the diagonals of kite KITE.
Explain why trapezoid MATH is not identified as a kite from the given information.
🚀 Choose Your Next Step
Do you need more support?
Return to the definitions and underline the key words. For a trapezoid, underline exactly one pair and parallel. For a kite, underline two pairs, consecutive, and congruent. Then use your physical models. The parallel sticks identify the trapezoid’s bases. Equal-length sticks that touch at a corner identify the kite’s congruent pairs.
Do you want an additional challenge?
Find two trapezoid-shaped and two kite-shaped objects or designs at home or in the community. Sketch each object. Add ∥, ≅, and ∠ symbols where appropriate, and write one sentence explaining why each sketch fits its classification.
🔓 Answer Keys
Show Answers to the Activity
Quick Check
Bases: MA and TH
Legs: AT and HM
Base-angle pairs:
∠M and ∠A
∠T and ∠H
Consecutive congruent-side pairs:
KI ≅ KE
IT ≅ ET
Diagonals: KT and IE
Explanation: Trapezoid MATH is not identified as a kite because the given information shows only that MA ∥ TH. There are no markings or statements indicating that MATH has two pairs of consecutive congruent sides.
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