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Why Are Vertically Opposite Angles Equal?

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Parallel and Intersecting Lines · Angles at an intersection · 3:10

You'll learn: A single equality proof needs the linear-pair deductions to remain visible.

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Why Are Vertically Opposite Angles Equal?

3:10

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Why Are Vertically Opposite Angles Equal?

You'll learn: A single equality proof needs the linear-pair deductions to remain visible.

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Same topic

Angles at an intersection

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Why Do Adjacent Angles on a Line Add to 180°?
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Why Do Adjacent Angles on a Line Add to 180°?
You'll learn: Adjacent angles that form a straight line together make 180°.

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Geometric facts versus measurements

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Why Does Measuring a Diagram Not Prove a Geometric Fact?
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Why Does Measuring a Diagram Not Prove a Geometric Fact?
You'll learn: Measuring a drawing can suggest a fact, but drawings are imperfect, so a proof is needed.

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Perpendicular lines

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Why Do Four Equal Intersection Angles Make Perpendicular Lines?
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Why Do Four Equal Intersection Angles Make Perpendicular Lines?
You'll learn: If four angles at an intersection are equal, each is 90°, so the lines are perpendicular.

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Parallel lines and segment intersections

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When Do Segments Meet—and What Happens If We Extend Them?
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When Do Segments Meet—and What Happens If We Extend Them?
You'll learn: Segments can meet at endpoints, midpoints or interior points, and extending them can create new meeting points.
Why Must Parallel Lines Lie in the Same Plane?
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Why Must Parallel Lines Lie in the Same Plane?
You'll learn: Lines that never meet but lie in different planes are not parallel; parallel lines must share a plane.

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Lines through paper folding

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Make Parallel and Perpendicular Creases by Folding
3:27
Make Parallel and Perpendicular Creases by Folding
You'll learn: Fold paper to make parallel and perpendicular creases and spot the repeating pattern.
Read Parallel-Line Arrows and Right-Angle Squares
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Read Parallel-Line Arrows and Right-Angle Squares
You'll learn: Arrows mark parallel lines and a small square marks a right angle in diagrams.

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Transversals and distinct angle measures

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Why Do Eight Transversal Angles Have at Most Four Measures?
3:27
Why Do Eight Transversal Angles Have at Most Four Measures?
You'll learn: A transversal makes eight angles from two vertically opposite pairs at each crossing, so at most four different measures.

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Corresponding angles and parallelism

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Find Corresponding Angles on Parallel Lines
3:32
Find Corresponding Angles on Parallel Lines
You'll learn: When lines are parallel, angles in matching positions at the two crossings are equal.
Use Corresponding Angles to Test Whether Lines Are Parallel
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Use Corresponding Angles to Test Whether Lines Are Parallel
You'll learn: If corresponding angles are equal the lines are parallel; if they differ, the lines meet somewhere.

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Drawing parallel lines

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Draw a Parallel Line with a Ruler and Set Square
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Draw a Parallel Line with a Ruler and Set Square
You'll learn: Slide a set square along a ruler to draw a line parallel to a given line.
Create Parallel Lines by Paper Folding
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Create Parallel Lines by Paper Folding
You'll learn: Fold paper twice at right angles to create parallel lines.

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Alternate and same-side interior angles

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Why Are Alternate Interior Angles Equal on Parallel Lines?
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Why Are Alternate Interior Angles Equal on Parallel Lines?
You'll learn: Alternate interior angles are equal because each equals the same corresponding angle.
Why Do Same-Side Interior Angles Add to 180°?
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Why Do Same-Side Interior Angles Add to 180°?
You'll learn: One same-side interior angle equals the angle forming a linear pair with the other, so the two add to 180°.
Find Missing Angles in a Parallel-Line Diagram
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Find Missing Angles in a Parallel-Line Diagram
You'll learn: Chain corresponding, alternate and linear-pair facts to find missing angles.