Mathematics
Grade 10
15 min
Proving a quadrilateral is a parallelogram
Proving a quadrilateral is a parallelogram
What you'll learn
- Solve one-step word problems involving multiplication of money amounts (up to $100) with 80% accuracy.
- Explain the steps used to solve a money multiplication word problem to a partner, using vocabulary such as 'product', 'multiply', and 'decimal'.
- Apply multiplication to determine the total cost of purchasing multiple items with given prices in a real-world scenario.
- Identify the correct operation (multiplication) needed to solve a money-related word problem from a set of mixed operation word problems with 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the five conditions that prove a quadrilateral is a parallelogram.
Construct a two-column proof to demonstrate that a quadrilateral is a parallelogram given certain properties.
Use the definition of a parallelogram (both pairs of opposite sides are parallel) to prove a quadrilateral is a parallelogram.
Apply theorems about sides, angles, and diagonals to prove a quadrilateral is a parallelogram.
Use coordinate geometry formulas (slope, midpoint, distance) to prove a quadrilateral is a parallelogram.
Solve for unknown variables that would make a given quadrilateral a parallelogram.
Ever see a wobbly gate or a leaning picture frame? 🖼️ Proving a shape is a perfect parallelogram is how engineers and designers ensure stability and precision in their...
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Key Concepts & Vocabulary
TermDefinitionExample
ParallelogramA quadrilateral where both pairs of opposite sides are parallel.In parallelogram ABCD, side AB is parallel to side DC, and side AD is parallel to side BC.
Opposite SidesIn a quadrilateral, two sides that do not share a common vertex (corner).In quadrilateral ABCD, the opposite sides are AB and DC, and also AD and BC.
Opposite AnglesIn a quadrilateral, two angles that do not share a common side.In quadrilateral ABCD, the opposite angles are ∠A and ∠C, and also ∠B and ∠D.
DiagonalA line segment that connects two non-consecutive vertices of a polygon.In quadrilateral ABCD, the diagonals are the segments AC and BD.
BisectTo cut a line segment into two congruent (equal length) parts.If point M is the midpoint of segment AC, then M bisects AC, and AM = MC.
Con...
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Core Formulas
Opposite Sides Congruent Theorem Converse
If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.
Use this when you are given or can prove that \overline{AB} ≅ \overline{DC} AND \overline{AD} ≅ \overline{BC}.
Opposite Angles Congruent Theorem Converse
If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram.
Use this when you are given or can prove that ∠A ≅ ∠C AND ∠B ≅ ∠D.
Diagonals Bisect Each Other Theorem Converse
If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Use this when you can show that the two diagonals share the same midpoint.
One Pair Parallel & Congruent Theorem
If one pair of opposite sides of a quadrilateral is both parallel and cong...
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Challenging
A quadrilateral has vertices A(0,0), B(a,b), C(a+c, b), and D(c,0). This shape is always a parallelogram. Which theorem is most easily demonstrated by the coordinate setup for sides AD and BC?
A.Both pairs of opposite angles are congruent.
B.The diagonals bisect each other.
C.One pair of opposite sides is both parallel and congruent.
D.Both pairs of opposite sides are parallel.
Challenging
Given that ABCD and ABEF are both parallelograms that share side AB. Which statement proves that quadrilateral CDEF is also a parallelogram?
A.CD || FE and CD ≅ FE
B.The diagonals CE and FD are congruent.
C.DE || CF and DE ≅ CF
D.The midpoint of CE is the same as the midpoint of FD.
Challenging
Having one pair of parallel opposite sides and one pair of congruent opposite sides is not sufficient to prove a quadrilateral is a parallelogram. Which shape is the classic counterexample to this flawed condition?
A.Rhombus
B.Rectangle
C.Isosceles Trapezoid
D.Kite
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Frequently asked questions
What grade level is "Proving a quadrilateral is a parallelogram"?
Proving a quadrilateral is a parallelogram is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Proving a quadrilateral is a parallelogram?
You'll be able to: Solve one-step word problems involving multiplication of money amounts (up to $100) with 80% accuracy; Explain the steps used to solve a money multiplication word problem to a partner, using vocabulary such as 'product'….
Is "Proving a quadrilateral is a parallelogram" 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 Proving a quadrilateral is a parallelogram?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.