Mathematics
Grade 10
15 min
Properties of trapezoids
Properties of trapezoids
What you'll learn
- Solve multiplication problems involving two decimals (up to hundredths) with at least 80% accuracy using a standard algorithm.
- Explain the process of multiplying two decimals, including how to determine the correct placement of the decimal point in the product, in their own words.
- Estimate the product of two decimals (up to tenths) before calculating, and compare their estimate to the actual product to check for reasonableness.
- Apply decimal multiplication to solve real-world word problems involving measurements, money, or other relatable scenarios.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify a trapezoid and its key parts (bases, legs, base angles, median).
State and apply the property that consecutive angles between parallel bases are supplementary.
Define an isosceles trapezoid and prove its key properties, including congruent base angles and congruent diagonals.
State and apply the Trapezoid Median Theorem to find unknown lengths.
Solve for unknown angles and side lengths in trapezoids using algebraic expressions.
Construct simple geometric proofs involving trapezoids.
Ever noticed the shape of a bridge's support structure or a classic handbag? 👜 You're likely looking at a trapezoid!
In this tutorial, we will explore the trapezoid, a unique member of the quadrilateral family. We will define its parts, uncover the specia...
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Key Concepts & Vocabulary
TermDefinitionExample
TrapezoidA quadrilateral with exactly one pair of parallel sides.In quadrilateral ABCD, if side AB is parallel to side DC, but side AD is not parallel to side BC, then ABCD is a trapezoid.
Bases and LegsThe parallel sides of a trapezoid are called the bases. The non-parallel sides are called the legs.In trapezoid ABCD with AB || DC, AB and DC are the bases, while AD and BC are the legs.
Base AnglesA pair of angles that share a common base. Every trapezoid has two pairs of base angles.In trapezoid ABCD with base DC, ∠D and ∠C form one pair of base angles. ∠A and ∠B form the other pair.
Isosceles TrapezoidA trapezoid in which the legs (non-parallel sides) are congruent.If trapezoid ABCD has AB || DC and the length of leg AD is equal to the length of leg BC, it is an is...
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Core Formulas
Consecutive Angles Property
In a trapezoid, consecutive angles between the two parallel bases are supplementary. If base₁ || base₂, then m∠A + m∠D = 180° and m∠B + m∠C = 180°.
Use this rule to find the measure of an unknown angle when you know the measure of the other angle sharing the same leg. This is a direct application of the Consecutive Interior Angles Theorem for parallel lines.
Isosceles Trapezoid Theorems
1. Base angles are congruent (e.g., ∠D ≅ ∠C and ∠A ≅ ∠B). 2. Diagonals are congruent (AC ≅ BD).
These properties apply ONLY to isosceles trapezoids. If you know a trapezoid is isosceles, you can assume these are true. Conversely, if a trapezoid has congruent base angles or congruent diagonals, you can prove it is isosceles.
Trapezoid Median Theorem
The length...
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Challenging
In trapezoid QRST with bases QR and ST, which of the following single pieces of information is sufficient to prove that QRST is an isosceles trapezoid?
A.The median is parallel to the bases.
B.The diagonals bisect each other.
C.pair of base angles are congruent.
D.pair of opposite sides are congruent.
Challenging
The vertices of a quadrilateral are A(0, 4), B(3, 5), C(5, 1), and D(0, -1). Which statement best describes quadrilateral ABCD?
A.It is an isosceles trapezoid.
B.It is a trapezoid, but not isosceles.
C.It is a parallelogram.
D.It is a kite.
Challenging
In isosceles trapezoid PQRS, PQ || SR. An altitude from P to base SR meets SR at point X. If PQ = 10, SR = 22, and the length of leg PS is 10, what is the height of the trapezoid (the length of PX)?
A.6
B.12
C.10
D.8
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Frequently asked questions
What grade level is "Properties of trapezoids"?
Properties of trapezoids is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Properties of trapezoids?
You'll be able to: Solve multiplication problems involving two decimals (up to hundredths) with at least 80% accuracy using a standard algorithm; Explain the process of multiplying two decimals, including how to determine the correct placement of….
Is "Properties of trapezoids" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Properties of trapezoids?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.