Download Math 350 Section 3.1 Answers to Classwork CW 1: An equilateral

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Math 350 Section 3.1 Answers to Classwork
CW 1: An equilateral triangle is a special case of an isosceles triangle, “all three sides
congruent” is a special case of “at least two sides congruent”. Also an equilateral triangle is a
special case of an acute triangle; all angles 60 degrees is a special case of all angles acute.
CW 2: (a) An isosceles right triangle is POSSIBLE; a triangle with sides 1, 1, and
2 is one.
(b) An equilateral right triangle is NOT POSSIBLE. All 3 angles must be congruent.
(c) A triangle with two right angles is NOT POSSIBLE. The angle sum would be > 180 degrees.
CW 3: (a) An isosceles triangle is acute. FALSE. One angle could be right or obtuse.
(b) An equilateral triangle is acute. TRUE. All angles are 60 degrees.
(c) An obtuse triangle is scalene. FALSE. A triangle with sides 1, 1, and 2 is obtuse but not scalene.
Classifying Quadrilaterals:
A. 1. Definition of Quadrilateral: A polygon with four sides. Numbers: All.
2. Definition of Trapezoid: A quadrilateral with exactly one pair of parallel sides.
Numbers: 3, 9, 13
3. Definition of Parallelogram: A quadrilateral with two pairs of parallel sides.
Numbers: 1, 4, 5, 6, 7, 10, 11, 15, 16
4. Definition of Rhombus: A quadrilateral with all four sides congruent.
Numbers: 4, 5, 11, 15
5. Definition of Rectangle: A quadrilateral with all four angles right angles.
Numbers: 4, 6, 7, 11, 15, 16
6. Definition of Square: A quadrilateral with all four sides congruent and all four angles right
angles. Numbers: 4, 11, 15
B. Hierarchy of Quadrilaterals:
Quadrilaterals (1 - 17)
Parallelograms (1, 4, 5, 6, 7, 10, 11, 15, 16)
Rhombi (4, 5, 11, 15)
Trapezoids (3, 9, 13)
Rectangles (4, 6, 7, 11, 15, 16)
Squares (4, 11, 15)
CW 4: (a). A rectangle is a parallelogram. TRUE; all rectangles shown (4, 6, 7, 11, 15, 16) are
also parallelograms.
(b) A rectangle is a square. FALSE; #6 is a counterexample
(c) A rhombus is a square. FALSE; #5 is a counterexample
(d) A square is a rhombus. TRUE; All squares shown (4, 11, 15) are also rhombi.
(e) A square is a rectangle. TRUE; All squares shown (4, 11, 15) are also rectangles.
(f) A rhombus is a parallelogram. TRUE; All rhombi shown (4, 5, 11, 15) are also
parallelograms.
CW 5: Decide whether each of these is possible or not. If it is, sketch a confirming example.
(a) A quadrilateral that is both a rectangle and a rhombus. POSSIBLE; Any square is.
(b) A parallelogram with a right angle. POSSIBLE; Any square or rectangle.
(c) A parallelogram with a pair of opposite sides that are not congruent. NOT POSSIBLE, by
the definition.
(d) A parallelogram with a pair of opposite angles that are not congruent. NOT POSSIBLE
(we will prove this in 3.3)
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