Diagonals in Geometry

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Questions and Answers

What is the definition of a diagonal?

  • A straight line that connects two adjacent corners of a polygon
  • A straight line that connects two opposite corners of a polygon (correct)
  • A curved line that connects two corners of a polygon
  • A line that divides a polygon into two equal parts

Why didn't Caroline's mother want her to cut across the intersection?

  • Because it wasn't safe (correct)
  • Because it was a diagonal
  • Because it was against the law
  • Because it was a quadrilateral

What type of diagonals cross each other at right angles?

  • Parallel diagonals
  • Skew diagonals
  • Mutually bisecting diagonals
  • Perpendicular diagonals (correct)

Which shapes in Diagram 1 have perpendicular diagonals?

<p>Kite and square (A)</p> Signup and view all the answers

What is the characteristic of mutually bisecting diagonals?

<p>They cross each other at the halfway point of each other (C)</p> Signup and view all the answers

Which shapes in Diagram 1 have mutually bisecting diagonals?

<p>Square and rectangle (C)</p> Signup and view all the answers

Why did Shirley decide to cut across the middle of the square?

<p>Because it would take a long time to go all the way around it (B)</p> Signup and view all the answers

What is a way to remember what perpendicular means?

<p>You can put the corner of a piece of paper right in it (A)</p> Signup and view all the answers

How many types of diagonals are mentioned in the text?

<p>Two (B)</p> Signup and view all the answers

What is the name of the ant who cut across the middle of the square?

<p>Shirley (A)</p> Signup and view all the answers

Flashcards

Diagonal

A straight line connecting two opposite corners of a polygon.

Perpendicular Diagonals

Diagonals that cross each other at right angles.

Kite and Square

Shapes with perpendicular diagonals in Diagram 1.

Mutually Bisecting Diagonals

Diagonals that cross each other at their midpoint.

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Square and Rectangle

Shapes with mutually bisecting diagonals in Diagram 1.

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Cutting Across Intersections

Not safe as indicated by Caroline's mother.

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Shirley's Decision

She chose to cut through the middle of the square for efficiency.

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Types of Diagonals

Two types mentioned: perpendicular and mutually bisecting.

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Safety at Intersections

Caroline's mother was concerned about safety in traffic areas.

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Shirley the Ant

The ant who chose to cut across the middle of the square.

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Study Notes

Diagonals

  • A diagonal is a straight line that connects two opposite corners of a polygon.

Types of Diagonals

  • There are two types of diagonals in polygons: perpendicular diagonals and mutually bisecting diagonals.

Perpendicular Diagonals

  • Perpendicular diagonals cross each other at a right angle (90 degrees).
  • A way to remember this is that you could fit the corner of a piece of paper exactly in the right angle.
  • Examples of shapes with perpendicular diagonals are kites and squares.

Mutually Bisecting Diagonals

  • Mutually bisecting diagonals cross each other at the halfway point of each other.
  • Examples of shapes with mutually bisecting diagonals are rectangles and squares.

Drawing Diagonals

  • To draw a diagonal, use a straight edge to draw a straight line from one corner to the opposite corner of a polygon.
  • By drawing two diagonals, you can determine if they are perpendicular or mutually bisecting.

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