Q:

# Please Fill in the BlanksGiven: Rectangle ABCDProve: AC¯¯¯¯¯≅BD¯¯¯¯¯A rectangle A B C D. Side A B and side C D are parallel. Side A D and B C are parallel. Diagonal B D and A C intersect each other at a point labeled as X.Statement ReasonRectangle ABCD GivenOpposite sides of a rectangle are congruent.DC¯¯¯¯¯≅DC¯¯¯¯¯ ∠ADC and ∠BCD are right angles. All right angles are congruent.△ADC≅△BCD SAS Congruence PostulateCPCTCAD¯¯¯¯¯≅BC¯¯¯¯¯AB¯¯¯¯¯≅DC¯¯¯¯¯AC¯¯¯¯¯≅BD¯¯¯¯¯∠ADC≅∠BCD∠ACD≅∠BDCDefinition of perpendicular linesTransitive Property of CongruenceReflexive Property of CongruenceDefinition of rectangle

Accepted Solution

A:
1)  Rectangle ABCD                Given2)AD=BC, DC=AB.                        Opposite sides of a rectangle are congruent.3)DC¯¯¯¯¯≅DC¯                              Reflexive property of Congruence4)∠ADC and ∠BCD are right angles.     Definition of rectangle.5)<ADC=<BCD.                                       All right angles are congruent.6)△ADC≅△BCD             SAS Congruence Postulate7)AC=BD.