Mathematics
Grade 10
15 min
Properties of parallelograms
Properties of parallelograms
What you'll learn
- Identify the correct operation (multiplication) needed to solve a word problem involving decimals and whole numbers in at least 4 out of 5 examples.
- Solve word problems involving multiplying decimals by whole numbers with at least 80% accuracy, showing all work.
- Explain the steps taken to solve a multiplication word problem involving decimals and whole numbers to a partner, including the placement of the decimal point in the final answer.
- Apply multiplication of decimals and whole numbers to create a real-world word problem that can be solved by a classmate.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the five key properties of parallelograms.
Apply the properties of parallelograms to find unknown side lengths and angle measures.
Use the properties of diagonals to solve for unknown values in a parallelogram.
Set up and solve algebraic equations based on the geometric properties of parallelograms.
Use coordinate geometry formulas (slope, distance) to verify that a given quadrilateral is a parallelogram.
Construct a basic two-column proof involving properties of parallelograms.
Have you ever noticed the pattern on a chain-link fence or the structure of a folding scissor lift? 🧐 You're looking at parallelograms in action!
This tutorial will explore the fundamental properties that define a parallelogram, a special type of quadrilateral. Und...
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Key Concepts & Vocabulary
TermDefinitionExample
ParallelogramA quadrilateral with two pairs of parallel opposite sides.In quadrilateral ABCD, if side AB is parallel to side DC and side AD is parallel to side BC, then ABCD is a parallelogram.
Opposite SidesIn a quadrilateral, sides that do not share a common vertex (corner).In parallelogram ABCD, AB and DC are opposite sides. AD and BC are also opposite sides.
Opposite AnglesIn a quadrilateral, angles that do not share a common side.In parallelogram ABCD, ∠A and ∠C are opposite angles. ∠B and ∠D are also opposite angles.
Consecutive AnglesAngles in a polygon that share a common side.In parallelogram ABCD, ∠A and ∠B are consecutive angles because they share side AB. Similarly, ∠B and ∠C are consecutive.
DiagonalA line segment that connects two non-consecutive vertic...
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Core Formulas
Opposite Sides Property
In a parallelogram, opposite sides are congruent. If ABCD is a parallelogram, then \( \overline{AB} \cong \overline{DC} \) and \( \overline{AD} \cong \overline{BC} \).
Use this rule to find the length of a side when you know the length of its opposite side, or to set up an equation if the side lengths are given as algebraic expressions.
Opposite Angles Property
In a parallelogram, opposite angles are congruent. If ABCD is a parallelogram, then \( \angle A \cong \angle C \) and \( \angle B \cong \angle D \).
Use this rule to find the measure of an angle when you know the measure of its opposite angle. This is also useful for setting up algebraic equations.
Consecutive Angles Property
In a parallelogram, consecutive angles are supplementary. For e...
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Challenging
In the provided two-column proof, what is the reason for Statement 2? Given: ABCD is a parallelogram. Prove: ∠A and ∠B are supplementary. Statement 1: ABCD is a parallelogram. Reason 1: Given. Statement 2: AB || DC and AD || BC. Reason 2: ?
A.Opposite sides of a parallelogram are congruent.
B.Definition of a parallelogram.
C.Consecutive angles are supplementary.
D.Alternate Interior Angles Theorem.
Challenging
In parallelogram ABCD, the diagonals intersect at E. The perimeter of ΔABE is 22. The length of side AB is 10. The length of diagonal AC is 12. What is the length of diagonal BD?
A.6
B.8
C.10
D.12
Challenging
In parallelogram JKLM, the ratio of the measure of angle J to the measure of angle K is 2:7. What is the measure of angle L?
A.40°
B.140°
C.20°
D.70°
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Frequently asked questions
What grade level is "Properties of parallelograms"?
Properties of parallelograms is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Properties of parallelograms?
You'll be able to: Identify the correct operation (multiplication) needed to solve a word problem involving decimals and whole numbers in at least 4 out of 5 examples; Solve word problems involving multiplying decimals by whole numbers with at….
Is "Properties of parallelograms" 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 parallelograms?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.