Question

The Euler diagram below accurately shows the relationship between five sets of quadrilaterals. Note: This assumes that a trapezoid is a quadrilateral with exactly one pair of parallel sides. Universal set: the set of all quadrilaterals Parallelograms Rectangles Rhombi Squares Trapezoids Create a modified version of this Euler diagram that incorporates the following two sets: • A: The set of all quadrilaterals that have reflection symmetry. B: The set of all quadrilaterals that have a non-trivial rotation symmetry.

          The Euler diagram below accurately shows the relationship between five sets of quadrilaterals.
Note: This assumes that a trapezoid is a quadrilateral with exactly one pair of parallel sides.
Universal set: the set of all quadrilaterals
Parallelograms
Rectangles
Rhombi
Squares
Trapezoids
Create a modified version of this Euler diagram that incorporates the following two sets:
• A: The set of all quadrilaterals that have reflection symmetry.
B: The set of all quadrilaterals that have a non-trivial rotation symmetry.

Show more…

The Euler diagram below accurately shows the relationship between five sets of quadrilaterals.
Note: This assumes that a trapezoid is a quadrilateral with exactly one pair of parallel sides.
Universal set: the set of all quadrilaterals
Parallelograms
Rectangles
Rhombi
Squares
Trapezoids
Create a modified version of this Euler diagram that incorporates the following two sets:
• A: The set of all quadrilaterals that have reflection symmetry.
B: The set of all quadrilaterals that have a non-trivial rotation symmetry.

Added by Tyler A.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Anthony Agnessanto

06/20/2020

Step 1

Step 1: Start by adding the sets A and B to the existing Euler diagram. Show more…

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The Euler diagram below accurately shows the relationship between five sets of quadrilaterals. Note: This assumes that a trapezoid is a quadrilateral with exactly one pair of parallel sides. Universal set: the set of all quadrilaterals Parallelograms Rhombi Trapezoids Rectangles Squares Create a modified version of this Euler diagram that incorporates the following two sets: A: The set of all quadrilaterals that have reflection symmetry B: The set of all quadrilaterals that have a non-trivial rotation symmetry

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Transcript

00:01 All right, so we're going to draw some quadrilaterals.

00:06 So we want them to have opposite sides or parallel.

00:10 So we can draw any kind of quadrororalogram we want.

00:14 We can have a square.

00:17 We could have a rectangle.

00:19 We could have a parallelogram.

00:22 We could have a rhombus.

00:25 And we could change the sizes of them.

00:29 We could make this parallelogram really.

00:33 Tall, we could make the rectangle really skinny.

00:40 Now you could find the angle measures of all these quadrilaterals that you drew.

00:49 The rectangles and the squares are easy because you know they're 90 degrees, but you're going to find that no matter the parallelogram that you draw, that these quadrilaterals have opposite angles that are congruent to each other.

01:10 So what that means is that if it's a parallelogram, the opposite angles are congruent.

01:22 So we're going to now prove the converse of that.

01:27 So we're going to try to prove that if opposite angles of a.

01:40 Quadrilateral are congruent, then opposite sides are parallel.

01:59 Great.

02:01 So we have to figure out what our given and our prove are...

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