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Please Fill in the Blanks

Given: Rectangle ABCD

Prove: 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 Reason
Rectangle ABCD Given
Opposite sides of a rectangle are congruent.
DC¯¯¯¯¯≅DC¯¯¯¯¯
∠ADC and ∠BCD are right angles.
All right angles are congruent.
△ADC≅△BCD SAS Congruence Postulate
CPCTC
AD¯¯¯¯¯≅BC¯¯¯¯¯AB¯¯¯¯¯≅DC¯¯¯¯¯AC¯¯¯¯¯≅BD¯¯¯¯¯∠ADC≅∠BCD∠ACD≅∠BDCDefinition of perpendicular linesTransitive Property of CongruenceReflexive Property of CongruenceDefinition of rectangle

Please Fill in the Blanks Given Rectangle ABCD Prove ACBD 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 class=

Respuesta :

1)  Rectangle ABCD                Given

2)AD=BC, DC=AB.                        Opposite sides of a rectangle are congruent.

3)DC¯¯¯¯¯≅DC¯                              Reflexive property of Congruence

4)∠ADC and ∠BCD are right angles.     Definition of rectangle.

5)<ADC=<BCD.                                       All right angles are congruent.

6)△ADC≅△BCD             SAS Congruence Postulate

7)AC=BD.                          









The statements and reasons that relate the given properties of the rectangle ABCD are given below.

From the given rectangle, we can deduce the following statements and their reasons;

  • Statement 1;  Rectangle ABCD

The reason is that it is given

  • Statement 2; AD ≅ BC and DC ≅ AB; This means that AD is congruent to BC and DC is congruent to AB. The congruent sides are opposite sides of the rectangle.

The reason is because; The opposite sides of a rectangle are congruent.

  • Statement 3; DC ≅ DC; This means DC is congruent to itself .                            

The reason is Reflexive property of Congruence

  • Statement 4; ∠ADC and ∠BCD are right angles. This means they are 90° and all angles in a rectangle are usually 90°.

The reason is from; definition of rectangle.

  • Statement 5; ∠ADC ≅ ∠BCD; We saw in statement 4 that they are both right angles.

The reason they are equal is because; All right angles are congruent.

  • Statement 6; △ADC ≅ △BCD; This means both triangles are congruent.        

The reason is from; SAS Congruence rule since the two corresponding side and included angle are equal to each other.

  • Statement 7; AC = BD;

The reason is because of CPCTC theorem which states that when two triangles are congruent, then every corresponding side of one triangle is equal to other one in the other triangle.

Read more at;    https://brainly.com/question/11673033      

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