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6-3 Tests for Parallelograms
ALGEBRA Find x and y so that the quadrilateral is a parallelogram.
18. SOLUTION: Opposite sides of a parallelogram are congruent.
Solve for x.
Solve for y.
19. SOLUTION: Opposite sides of a parallelogram are congruent.
Solve for x.
Solve for y.
20. SOLUTION: Opposite angles of a parallelogram are congruent.
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Alternate interior angles are congruent. Page 1
6-3 Tests for Parallelograms
20. SOLUTION: Opposite angles of a parallelogram are congruent.
Alternate interior angles are congruent. Use substitution.
Substitute
in
.
ALGEBRA Find x and y so that the quadrilateral is a parallelogram.
23. SOLUTION: Opposite sides of a parallelogram are congruent.
So,
and
.
Solve for x in terms y.
Substitute
in
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.
Page 2
6-3 Tests for Parallelograms
ALGEBRA Find x and y so that the quadrilateral is a parallelogram.
23. SOLUTION: Opposite sides of a parallelogram are congruent.
So,
and
.
Solve for x in terms y.
in
Substitute
Substitute
in
.
to solve for x.
So, x = 4 and y = 3.
COORDINATE GEOMETRY Graph each quadrilateral with the given vertices. Determine whether the
figure is a parallelogram. Justify your answer with the method indicated.
24. A(–3, 4), B(4, 5), C(5, –1), D(–2, –2); Slope Formula
SOLUTION: eSolutions Manual - Powered by Cognero
Page 3
Substitute
in
to solve for x.
6-3 Tests
So, x for
= 4Parallelograms
and y = 3.
COORDINATE GEOMETRY Graph each quadrilateral with the given vertices. Determine whether the
figure is a parallelogram. Justify your answer with the method indicated.
24. A(–3, 4), B(4, 5), C(5, –1), D(–2, –2); Slope Formula
SOLUTION: Since both pairs of opposite sides are parallel, ABCD is a parallelogram.
25. J(–4, –4), K(–3, 1), L(4, 3), M (3, –3); Distance Formula
SOLUTION: Since the pairs of opposite sides are not congruent, JKLM is not a parallelogram.
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Page 4
6-3 Tests for Parallelograms
25. J(–4, –4), K(–3, 1), L(4, 3), M (3, –3); Distance Formula
SOLUTION: Since the pairs of opposite sides are not congruent, JKLM is not a parallelogram.
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Page 5
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