Classifying Shapes by Lines and Angles

Lesson 1 of 1: Properties, Not Names

In this lesson:

• Sort shapes by parallel and perpendicular sides
• Classify triangles as acute, right, or obtuse
• Read "is-a" relationships straight off a property chart

What You Will Be Able To Do

You will be able to:

1. Classify shapes by parallel sides: two, one, or none.
2. Classify shapes by perpendicular sides and angle type.
3. Classify every triangle as acute, right, or obtuse.
4. Identify right triangles as their own category.
5. Reason from properties to a shape's name.

Describe a Shape Without Its Name

• Quick check: lines that never meet (parallel) and lines that cross in a square corner (perpendicular) — point to each and say how you know.
• The real challenge: describe a rectangle using only its properties, no name, precisely enough that someone draws a rectangle and nothing else.

Sort These Figures by Parallel Pairs

The set: rectangle, square, parallelogram, rhombus, trapezoid, right trapezoid, right triangle, irregular quadrilateral.

• Two pairs of parallel sides
• One pair of parallel sides
• Zero pairs of parallel sides

Which column does each figure belong in?

"Two Pairs of Parallel Sides" Makes a Parallelogram

Every figure in the "Two Pairs" column is a parallelogram — that's the definition.

Re-Sort the Same Figures by Perpendicular Sides

Can a figure have parallel sides but no perpendicular sides? Yes — the parallelogram.

Some Figures Belong to Both Groups at Once

• Rectangles and squares have parallel sides and perpendicular sides.
• The parallelogram has parallel sides only — no right angles.
• The right triangle has perpendicular sides only — no parallel sides.

Classify Four Figures by Both Properties

For each figure, decide: parallel sides? perpendicular sides?

• A square
• A general parallelogram
• A right triangle
• An obtuse triangle

Check both questions separately before you answer.

Does This Sorting Tool Work on Triangles Too?

You've been checking two things: parallel sides and perpendicular sides.

• No triangle can ever have parallel sides — three sides that close a shape must intersect.
• But triangles absolutely can have perpendicular sides — you just found one.

The same two checks work. Only one answer changes.

Five Unlabeled Triangles — What Would Sort These?

Look at each angle in each triangle. What natural groups do you see?

Testing Each Triangle Against the Corner

Right Triangles: the Only Triangles with Perpendicular Sides

• Every triangle is exactly one type — acute, right, or obtuse.
• A right triangle has exactly one right angle; the other two are acute.
• Those two sides forming the right angle are perpendicular — the only such pair in any triangle.

Predict First: Right Triangle, or Just Close?

• (a) This is a right triangle
• (b) This looks close, but it isn't

Why "Looks Right" Isn't Enough — Always Test

• The marked angle in the decoy triangle measured 85 degrees — close, but not a match.
• Only the paper-corner test can tell 85, 90, and 95 degrees apart reliably.
• A triangle has at most one right angle — if none matches exactly, it isn't a right triangle.

Find the One Right Triangle Among Four

• Test each candidate's marked angle against the paper corner.
• Only one will match exactly.

Draw and Label a Right Triangle

• Draw any right triangle — any size, any orientation.
• Mark the right angle with a small square symbol.
• Label the two sides that form the right angle as perpendicular.

Rotate your triangle. Is it still a right triangle? Why?

One Property Isn't Always Enough

• A rhombus and a square can both have "all sides equal" — checked.
• A rectangle and a square can both have "all right angles" — checked.
• One property at a time can't always tell two figures apart.

What if we checked every property at once?

The Property Chart: Five Figures, Five Questions

Five figures. Five yes-or-no questions each. Twenty-five boxes to fill in.

Filling In the Rectangle and Square Rows

Predict First: Is a Square a Rectangle?

• (a) Yes — a square is a rectangle
• (b) No — they are two separate shapes

Look back at both rows before you decide.

Reading "Is-A" Straight Off the Chart

• The square matches every rectangle property, plus one more.

A Tilted Rectangle Is Still a Rectangle

• Rotating a figure never changes its properties — only its orientation.
• Check parallel sides, right angles, and perpendicular sides — not the silhouette.
• A parallelogram that "looks" rectangular still needs its angles tested.

Always, Sometimes, or Never True?

• "A parallelogram has right angles."
• "A rectangle has perpendicular sides."
• "A triangle has parallel sides."
• "A trapezoid has exactly one pair of parallel sides."

Decide each: Always, Sometimes, or Never — before the next slide.

Right Trapezoids Still Count as Trapezoids

• A right trapezoid has exactly one pair of parallel sides — the trapezoid definition, satisfied.
• Its leg is perpendicular to both parallel sides, creating two right angles, not one.
• The definition is about parallel sides, never about angles.

Solo Commit: Solve a Mystery-Figure Riddle

"I have two pairs of parallel sides, no right angles, and all four sides equal. What am I?"

Write your answer on your own before we discuss.

Reverse Direction: Given Only Properties, Draw the Figure

Draw a figure that has:

• Exactly one pair of parallel sides
• Two right angles
• No pair of sides equal in length

No name given — properties only. What did you draw?

Four Mistakes Worth Double-Checking Today

A square passes every rectangle test, plus one more — it is a rectangle.
Check the properties, not the tilt or the silhouette.
If it isn't tested with the corner, it isn't confirmed right.
The trapezoid definition is about parallel sides, not about angles.

Key Takeaways From Today's Lesson

✓ Classify by properties — parallel, perpendicular, angle type — not by name.
✓ Right triangles are the only triangles with perpendicular sides.
✓ A figure can belong to more than one category at once.
✓ A property chart lets you compare figures and read "is-a" relationships directly.

Coming Up Next: Finding Lines of Symmetry

In the next lesson, you'll ask a new question about these same figures: does it fold onto itself perfectly? The same habit of mind applies — check, don't assume, even when a figure is rotated or looks unfamiliar.