Unit 10: 2D Shapes
Unit 10: 2D Shapes
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Categorizing Triangles by Their Angles:
Categorizing Triangles by Their Angles:
1) A right triangle has one right angle (90°).
1) A right triangle has one right angle (90°).
2) An acute triangle has 3 acute angles
(<90°).
2) An acute triangle has 3 acute angles
(<90°).
3) An obtuse triangle has 1 obtuse angle
(>90° and <180°).
3) An obtuse triangle has 1 obtuse angle
(>90° and <180°).
Categorizing Triangles by Side Length:
Categorizing Triangles by Side Length:
1) An equilateral triangle has
3 equal sides.
1) An equilateral triangle has
3 equal sides.
2) An isosceles triangle has
2 equal sides.
2) An isosceles triangle has
2 equal sides.
3) A scalene triangle has no
equal sides.
3) A scalene triangle has no
equal sides.
Drawing triangles based on side length and angles:
Drawing triangles based on side length and angles:
You may be asked to draw a triangle after being given clues about their side lengths and angles. Follow these steps when doing this task:
You may be asked to draw a triangle after being given clues about their side lengths and angles. Follow these steps when doing this task:
1) Decide what the words mean!
1) Decide what the words mean!
ex. An acute equilateral triangle = all 3 angles are acute, all 3 sides are the same length.
ex. An obtuse isosceles triangle = 1 angle is an obtuse angle, 2 side lengths are equal.
ex. A right scalene triangle = 1 angle is a right angle, all 3 sides are different lengths.
2) Start by drawing the appropriate angle (either right, obtuse or acute).
2) Start by drawing the appropriate angle (either right, obtuse or acute).
3) Use the clues given in the questions to draw the next step(s):
3) Use the clues given in the questions to draw the next step(s):
ex. If 2 side lengths are the same, measure with a ruler to ensure they are equal.
ex. If all side lengths are different, extend one line so it is longer than the other.
ex. If given a specific angle found in the triangle, measure that angle as your next step.
4) Connect all 3 angles/sides to finish drawing your triangle!
4) Connect all 3 angles/sides to finish drawing your triangle!
5) Double check your drawing. Does it have the correct angles and side lengths?
5) Double check your drawing. Does it have the correct angles and side lengths?
Polygons:
Polygons:
A polygon is a closed 2-D figure with straight line segments that intersect at vertices. A polygon does not have any curved or broken lines. See the photo below for examples of polygons:
A polygon is a closed 2-D figure with straight line segments that intersect at vertices. A polygon does not have any curved or broken lines. See the photo below for examples of polygons:
Regular polygons have all equal side lengths and all equal angles. See the photo for examples!
Regular polygons have all equal side lengths and all equal angles. See the photo for examples!
In each shape, all of the sides are equal. Additionally, in each shape, all of the angles are equal.
Irregular polygons do not have all equal side lengths and all equal angles (some is ok, but not all).
Irregular polygons do not have all equal side lengths and all equal angles (some is ok, but not all).
If the side lengths are the same, some angles must be different.
If the angles are the same, some side lengths must be different.
Sometimes, some of the side lengths and the angles are different!
Sometimes it is a shape we recognize (like a rectangle or a trapezoid) and sometimes it is a shape that does not have a name.
Congruency:
Congruency:
Two polygons are congruent if they are identical in size and shape.
Two polygons are congruent if they are identical in size and shape.
The polygons must have the same side lengths and the same angle measures to be congruent. They are exact copies!
The polygons must have the same side lengths and the same angle measures to be congruent. They are exact copies!
Two polygons are similar if they are the same shape, but their size is different.
Two polygons are similar if they are the same shape, but their size is different.
Congruent figures are always similar, but similar figures are not always congruent!
Congruent figures are always similar, but similar figures are not always congruent!
In this example, the yellow and blue triangles are congruent. They are the same shape and size.
However, the red triangle is similar to the yellow and blue triangles. They are the same shape, but different sizes!
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