Unit 6 Quadrilaterals Section 6.5 Properties of Rhombi and Squares

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Unit 6 Quadrilaterals Section 6.5 Properties of Rhombi and Squares

* * parallel congruent CONGRUENT congruent supplementary parallelogram 4 equal sides parallel congruent * CONGRUENT congruent supplementary = 180 4 ≅ right triangles bisect each other * ARE PERPENDICULAR

180 – ____ – ____ = 32o 90o 58o 180 – ____ – ____ = 58o 58o 32o 90o

180 – ____ – ____ = 32o 90o 58o 90o 60o 58o 58o 120o 30o 32o 90o 30o

diagonal side 26 Diagonal part 26 26 26 26 10 24

diagonal side side 26 _____ = _____ 2x + 4 4x – 4 26 26 –2x –2x 4 = part _____ = _____ 2x + 4 4x – 4 26 12 26 –2x –2x 12 4x – 4 = 12 4 = 2x – 4 26 +4 +4 2x + 4 10 2(4) + 4 = 8 = 2x 26 24 P= 4(12) 12 x = 4 = 48 2 2

diagonal side side 26 _____ = _____ 2x + 4 4x – 4 26 26 –2x –2x 4 = part _____ = _____ 2x + 4 4x – 4 26 8 26 –2x –2x 8 4x – 4 = 8 4 = 2x – 4 26 +4 +4 2x + 4 10 2(4) + 4 = 8 = 2x 26 24 P= 4(12) 12 x = 4 = 48 2 2 diagonal part whole diagonal 8 8 3y – 1 = 8 +1 +1 3y = 9 3 3 y = 3

diagonal side side 26 _____ = _____ 2x + 4 4x – 4 26 26 –2x –2x 4 = part _____ = _____ 2x + 4 4x – 4 26 8 26 –2x –2x 8 4x – 4 = 8 4 = 2x – 4 26 +4 +4 2x + 4 10 2(4) + 4 = 8 = 2x 26 24 P= 4(12) 12 x = 4 = 48 2 2 diagonal part diagonal part whole diagonal whole diagonal 13 8 a2 + b2 = c2 8 3y – 1 = 8 13 ? +1 +1 13 52 + 122 = c2 13 c 3y = 9 12 25 + 144 = c2 P = 4(13) 3 3 169 = c2 y = 3 P = 52 5

parallelogram rhombus rectangle

parallel congruent are congruent congruent right angles supplementary parallelogram rhombus rectangle 90 90 parallel congruent are congruent 90 90 congruent right angles supplementary = 180

parallel congruent are congruent congruent right angles supplementary parallelogram rhombus rectangle 90 90 parallel congruent are congruent 90 90 congruent right angles 45 45 supplementary 4 ≅ right isosceles triangles = 180 bisect each other 45 are congruent 45 are perpendicular

parallelogram diagonals bisect rhombus rectangle diagonals bisect diagonals bisect and diagonals are ⊥ and diagonals are ≅ diagonals bisect, are ≅, and are ⊥ square

4 16 16 in 16 in 45 45 22.6 in 11.3 in 90o 45o 16 16 45o 90o a2 + b2 = c2 45 162 + 162 = c2 45 256 + 256 = c2 512 = c2 16