Vocabulary rectangle rhombus square Helpful Hint Rectangles, rhombi, and squares are sometimes referred to as special parallelograms. They have all the properties of a parallelogram plus additional ones that identify them as a special parallelogram. Helpful Hint

DEFINITIONS A BICONDITIONAL STATEMENT WILL PROVIDE OF AND FOR PROPERTIES…

ADDITIONAL RHOMBI OF/FOR RULES

ADDITIONAL RECTANGLE OF/FOR RULES

RHOMBUS OF/FOR PROPERTIES Properties OF Rhombus: rhombus → 4  sides rhombus →  diagonals rhombus → diagonals bisect corner ’s rhombus → llgram Properties FOR Rhombus: 4  sides → rhombus llgram with  diagonals → rhombus llgram with diagonals bisect corner ’s → rhombus

RECTANGLE OF/FOR PROPERTIES Properties OF Rectangle: rectangle → 4 right ’s rectangle →  diagonals rectangle → llgram Properties FOR Rectangle: 4 right ’s → rectangle llgram with  diagonals → rectangle

Example 1a: Using Properties of Rhombuses to Find Measures TVWX is a rhombus. Find TV and mVTZ.

Example 1b: Using Properties of Rhombuses to Find Measures Given rhombus ABCD, find the angles:

Example 2: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.

Check It Out! Example 3 The vertices of STVW are S(–5, –4), T(0, 2), V(6, –3) , and W(1, –9) . Find the most specific name for quadrilateral STVW. Check if the diags bisect each other (llgram). Check if the diags are congruent (rect). Check if the diags are perpendicular (rhom). Must be llgram to be rect or rhom, must be all 3 to be a square.

Example 4: Applying Conditions for Special Parallelograms Determine if the conclusion is valid. If not, tell what additional information is needed to make it valid. Given: Conclusion: EFGH is a rhombus. The conclusion is not valid. By Theorem 6-5-3, if one pair of consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus. By Theorem 6-5-4, if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. To apply either theorem, you must first know that ABCD is a parallelogram.

Check It Out! Example 4 Given: PQTS is a rhombus with diagonal Prove:

Lesson Quiz: Part IV 6. Given: ABCD is a rhombus. Prove: 

Lesson Quiz: Part III 1. Use the diagonals to determine whether a quadrilateral with vertices A(2, 7), B(7, 9), C(5, 4), and D(0, 2) is a llgram, rectangle, rhombus, or square. Give all the names that apply. 2. Given rectangle QRST, find all angles:

Lesson Quiz: Part III 3. The vertices of ABCD are A(1, 3), B(3, 2), C(4, 4), and D(2, 5). Classify the quadrilateral. 4. Given: ABCD is a rhombus. Prove:

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