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Show that TWVU is a parallelogram by proving both pairs of opposite sides congruent. PowerPoint Presentation
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Show that TWVU is a parallelogram by proving both pairs of opposite sides congruent. - PowerPoint PPT Presentation


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Placing Figures in the Coordinate Plane. LESSON 6-6. Additional Examples. Show that TWVU is a parallelogram by proving both pairs of opposite sides congruent. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram by Theorem 6-6. .

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Placing Figures in the Coordinate Plane

LESSON 6-6

Additional Examples

Show that TWVU is a parallelogram by proving both pairs of opposite sides congruent.

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram by Theorem 6-6.

You can prove that TWVU is a parallelogram by showing that TW = VU and WV = TU. Use the Distance Formula.

slide2

TW = (a + c – a)2 + (b + d – b)2 =

VU = (c + e – e)2 + (d – 0)2 =

WV = ((a + c) – (c + e))2 + (b + d – d)2 =

TU = (a – e)2 + (b – 0)2 =

(a – e)2 + b2

(a – e)2 + b2

c2 + d2

c2 + d2

Placing Figures in the Coordinate Plane

LESSON 6-6

Additional Examples

(continued)

Use the coordinates T(a, b), W(a + c, b + d), V(c + e, d), and U(e, 0) that you found in Example 2.

Because TW = VU and WV = TU, TWVU is a parallelogram.

Quick Check

slide3

Because AB || CO and CO is horizontal, AB is also horizontal. So point B has the same second coordinate, q, as point A.

Placing Figures in the Coordinate Plane

LESSON 6-6

Additional Examples

Use the properties of parallelogram OCBA to find the missing coordinates. Do not use any new variables.

The vertex O is the origin with coordinates O(0, 0).

Because point A is p units to the left of point O, point B is also p units to the left of point C because OCBA is a parallelogram. So the first coordinate of point B is –p – x.

The missing coordinates are O(0, 0) and B(–p – x, q).

Quick Check