Geometry Chapter 6 Note Sheets
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6.3 Tests for Parallelograms Notes
Identify Parallelograms Example 1: Determine whether the
quadrilateral is a parallelogram. Justify your answer.
Guided Practice 1: Which method would prove the quadrilateral is
a parallelogram?
A. Both pairs of opp. sides ||. B. Both pairs of opp. sides ≅
.C. C. Both pairs of opp. ∠s ≅. D. One pair of opp. sides both ||
and ≅.
Geometry Chapter 6 Note Sheets
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Use Parallelograms and Algebra to Find Values Example 3: Find x
and y so that the quadrilateral is a parallelogram. Guided Practice
3: A. Find m so that the quadrilateral is a parallelogram.
B. If !" = !"− !, !" = !"+ !, !" = !"− !, and !" = !"+ !, find !
and ! so that the quadrilateral is a parallelogram.
Geometry Chapter 6 Note Sheets
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Example 4: COORDINATE GEOMETRY Graph Quadrilateral QRST has
vertices Q(–1, 3), R(3, 1), S(2, –3), and T(–2, –1). Determine
whether the quadrilateral is a parallelogram. Justify your answer
by using the Slope Formula. Guided Practice 4: Graph quadrilateral
EFGH with vertices E(–2, 2), F(2, 0), G(1, –5), and H(–3, –2).
Determine whether the quadrilateral is a parallelogram. Example
5:
A student is given the following information and then asked to
write a paragraph proof. Determine which statement would correctly
complete the student’s proof.
Given: Parallelogram !"#$ and Parallelogram !"#$ Prove: ∠! ≅
∠!
Proof: We are given Parallelogram !"#$ and Parallelogram !"#$.
Since opposite angles of a parallelogram are congruent, ∠! ≅ ∠! and
∠! ≅ ∠!. __________________.
A. Therefore, ∠! ≅ ∠! by the Transitive Property of Congruence.
B. Therefore, ∠! ≅ ∠! by the Transformative Property of Congruence.
C. Therefore, ∠! ≅ ∠! by the Reflective Property of Congruence. D.
Therefore, ∠! ≅ ∠! by the Reflexive Property of Congruence.