SPECIAL TYPE OF PARALLELOGRAM 6.5 SQUARES. A quadrilateral with 4 congruent sides Characteristics of a square: Both sets of opp. sides are congruent and.

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Presentation transcript:

SPECIAL 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 m  WZX = 39.5, find m  ZYX. 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 m  CDB if m  ABC = 126. B. ABCD is a rhombus. If BC = 4x – 5 and CD = 2x + 7, find x.

QRST is a square. Find n if m  TQR = 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.