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.