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Why Does Measuring a Diagram Not Prove a Geometric Fact?

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Parallel and Intersecting Lines · Geometric facts versus measurements · 3:38

You'll learn: Measuring a drawing can suggest a fact, but drawings are imperfect, so a proof is needed.

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Why Does Measuring a Diagram Not Prove a Geometric Fact?

3:38

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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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Next topic

Perpendicular lines

1

Why Do Four Equal Intersection Angles Make Perpendicular Lines?
3:22
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.

Next topic

Parallel lines and segment intersections

2

When Do Segments Meet—and What Happens If We Extend Them?
3:22
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?
3:15
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.

Next topic

Lines through paper folding

2

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
3:37
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.

Next topic

Transversals and distinct angle measures

1

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.

Next topic

Corresponding angles and parallelism

2

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
3:26
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.

Next topic

Drawing parallel lines

2

Draw a Parallel Line with a Ruler and Set Square
3:21
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
3:24
Create Parallel Lines by Paper Folding
You'll learn: Fold paper twice at right angles to create parallel lines.

Next topic

Alternate and same-side interior angles

4

Why Are Alternate Interior Angles Equal on Parallel Lines?
3:13
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°?
3:21
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
3:08
Find Missing Angles in a Parallel-Line Diagram
You'll learn: Chain corresponding, alternate and linear-pair facts to find missing angles.
Draw an Extra Parallel Line to Unlock an Angle Problem
3:08
Draw an Extra Parallel Line to Unlock an Angle Problem
You'll learn: Drawing an extra parallel line through a corner turns a hard angle problem into known angle pairs.

Next topic

Parallel illusions

1

Are These Lines Really Parallel—or Is It an Illusion?
3:22
Are These Lines Really Parallel—or Is It an Illusion?
You'll learn: Optical illusions can make parallel lines look bent; check with measurements and angle facts.