Rectangles, Rhombuses and Squares PDF

Rectangles, Rhombuses and Squares J. S o r i a n o , L P T G a br i e l l e  tencies Learn that these geometric shapes Compe are special parallelograms; Identify the theorems on the different kinds of paral...

Rectangles, Rhombuses and Squares J. S o r i a n o , L P T G a br i e l l e  tencies Learn that these geometric shapes Compe are special parallelograms; Identify the theorems on the different kinds of parallelograms; Solve problems involving the difference kinds of parallelograms.  Special Parallelograms Rectangles, rhombuses and squares are called special parallelograms. It means that the properties of a parallelogram are true for each geometric figure.  Definition A rectangle is a parallelogram with four right angles. A rhombus is a parallelogram g l e R ec t a n with four congruent sides. A square is a parallelogram h o m b u s R with four right angles and four r e S qu a congruent sides.  B C Theorem 5. 2a g le n a l s o f a R e c t a n Dia g o D A m i s a r e c t a n g le , If a p a r a lle lo g r a ls a r e c o ng r u e nt. then i t s di a g o na  Theorem 5.2b Diagonals of a Rhombus R S If a parallelogram is a rhombus, then its diagonals are U perpendicular. P T  Theorem 5.2c R S If a parallelogram is a rhombus, then each diagonals bisects a pair of opposite angles. U P T  B C Theorem 5.2d he d i a g o na le s o f a If t nt , t h e n D lo g r a m a r e c o ng r u e A para lle t a n g le. a lle lo g r a m i s a r e c the p a r  Theorem 5.2e If the diagonals of a R S parallelogram are perpendicular, then the parallelogram is a rhombus. U P T  Theorem 5.2f R S If the diagonals of a parallelogram bisect both pairs of opposite angles, then the U parallelogram is a rhombus. P T TRY IT! Name the special parallelogram. Explain your answer. 3 S R 3 3 T P 3 Name the special parallelogram. Explain your answer. 3 O M 3 H E Name the special parallelogram. Explain your answer. 3 I T 2.5 2.5 K E 3  ∎PLAN is a rhombus. If m∠PLA=60, find the following measures. L a. m∠ = P A S N  ∎PLAN is a rhombus. If m∠PLA=60, find the following measures. L b. m∠ = P A S N  ∎PLAN is a rhombus. If m∠PLA=60, find the following measures. L c. m∠ = P A S N  ABCD is a rhombus. B A a. m∠ = (4 − 15)° m∠ = ( + 21)° E m∠ = ____________ D C  ABCD is a rhombus. B A b. ∠ ≅ ∠ AB = 5x + 6 E BC = x +14 AD = _____________ D C  WXYZ is a rectangle. X Y c. XZ = 2x - 9 YW = x + 12 YW = _____________ A W Z  WXYZ is a square. X Y d. WA = 3x AY = x + 6 XZ = __________ A W Z  Thanks! see you tomorrow! PREPARE FOR SEATWORK TOMORROW AND QUIZ ON FRIDAY