SPEC IAL TYPE OF PARALLELOGRAM

6.5 SQUARES

• A quadrilateral with 4 congruent sides

• Characteristics of a square:• Both sets of opp. sides are

congruent and parallel• Both sets of opp. angles are

congruent• Diagonals bisect each other• Diagonals split it into 2

congruent triangles• Consecutive angles are

supplementary• If an angle is a right angle then

all 4 angles are right angles• Diagonals bisect the pairs of

opposite angles• Diagonals are perpendicular

• A square is a rhombus and a rectangle.

LESSON 6.5 : RHOMBI (SPECIAL TYPE OF PARALLELOGRAM)

• A quadrilateral with 4 congruent sides

• Characteristics of a rhombus:• Both sets of opp. sides are

congruent and parallel• Both sets of opp. angles are

congruent• Diagonals bisect each other• Diagonals split it into 2

congruent triangles• Consecutive angles are

supplementary• If an angle is a right angle then

all 4 angles are right angles

• In a rhombus:• Diagonals are perpendicular• Diagonals bisect the pairs of

opposite angles

KITE

• Two sets of consecutive sides are congruent• Diagonals are

perpendicular

A. The diagonals of rhombus WXYZ intersect at V.If mWZX = 39.5, find mZYX.

B. The diagonals of rhombus WXYZ intersect at V. If WX = 8x – 5 and WZ = 6x + 3, find x.

A. ABCD is a rhombus. Find mCDB if mABC = 126.

B. ABCD is a rhombus. If BC = 4x – 5 and CD = 2x + 7, find x.

QRST is a square. Find n if mTQR = 8n + 8.

QRST is a square. Find QU if QS = 16t – 14 and QU = 6t + 11.

Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for A(–2, –1), B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain.