Two triangles are shown to be congruent by identifying a combination of translations, rotations, or reflections that move one figure onto the other. if δmap ≅ δcar, which angle must be congruent to ∠arc? why?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

5. which description does not guarantee that a quadrilateral is a squar ajo is a parallelogram with perpendicular diagonals 0% has all sides congruent and all angles congruent o has all right angles and has all sides congruent 10% is both a rectangle and a rhombus 30%

Griffin ordered a pair of sneakers online. he had a $22 credit that he applied toward the purchase, and then he used a credit card to pay for the rest of the cost. if the shoes cost $58, how much did griffin charge to his credit card when he bought the sneakers?