Notes

Acute triangles have
3 acute angles (angles that measure between 0° and 90°).
Right triangles have
1 right angle (an angle that measures 90°).
Obtuse triangles have
1 obtuse angle (an angle that measures between 90° and 180°).


Triangles also can be classified according to their side lengths.

Triangles are most often classified with both the side-length and angle-measure classifications.
Combine the terms in the table to classify each triangle onscreen. For example, “scalene right triangle.”
scalene acute triangle
isosceles right triangle
equilateral obtuse triangle


Take one more look before revealing the answers.
Have you considered the side lengths carefully and used the correct terms?
Have you paid close attention to all the angles and used the correct terms?

Let’s take a closer look:
Notice that the trapezoid stands alone and is not part of the family of quadrilaterals that are parallelograms.
The trapezoid can only have one pair of parallel sides. All parallelograms have 2 pairs of parallel sides.

Another thing we can see is that the most specialized quadrilateral is the square. When you consider parallel sides, side lengths, and angle measures, the square has it all:
2 pairs of parallel sides from the parallelogram
4 equal side lengths from the rhombus
4 angles that measure 90° from the rectangle


If you know the order in this hierarchy, you can determine whether statements such as these are true or false:
All squares are rectangles.
All trapezoids are parallelograms.
All parallelograms are quadrilaterals.
All rectangles are rhombuses.
All squares are rhombuses.
All trapezoids are quadrilaterals.
All parallelograms are rectangles.
For each of these statements, record “true” or “false” before going to the next screen.


Take another look at each statement and your responses then reveal the answers. Did you accurately interpret the hierarchy when answering?
All squares are rectangles. Answer
All trapezoids are parallelograms. Answer
All parallelograms are quadrilaterals. Answer
All rectangles are rhombuses. Answer
All squares are rhombuses. Answer
All trapezoids are quadrilaterals. Answer
All parallelograms are rectangles. Answer


Be sure to take some time to review the definitions for all the types of triangles and quadrilaterals. You can use the keywords.
Knowing the definitions and the classifications of triangles and quadrilaterals as well as the quadrilateral hierarchy will be very helpful as you continue your study of math, especially in topics related to geometry.