Geometry Unit 6 Note Sheets

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6.3 Tests for Parallelograms Notes

Geometry Unit 6 Note Sheets

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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 #.

Mores Examples: Determine whether the quadrilateral is a parallelogram. Justify your answer.

1. 2.

3.

Geometry Unit 6 Note Sheets

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Use Parallelograms to Prove Relationships Example 2: MECHANICS Scissor lifts, like the platform lift shown, are commonly applied to tools intended to lift heavy items. In the diagram, �A # �C and �B # �D. Explain why the consecutive angles will always be supplementary regardless of the height of the platform.

Guided Practice 2: The diagram shows a car jack used to raise a car from the ground. In the diagram, AD # BC and AB # DC. Based on this information, which statement will be true, regardless of the height of the car jack.

Use Parallelograms and Algebra to Find Values Example 3: Find x and y so that the quadrilateral is a parallelogram.

Guided Practice 3: Find m so that the quadrilateral is a parallelogram.

Geometry Unit 6 Note Sheets

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More Examples:

4. If 𝐹𝐾 = 3𝑥 − 1, 𝐾𝐺 = 4𝑦 + 3, 𝐽𝐾 = 6𝑦 − 2, and 𝐾𝐻 = 2𝑥 + 3, find 𝑥 and 𝑦 so that the quadrilateral is a parallelogram.

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.