Question

Use two 2-Column proofs to show that either diagonal of a rectangle will create two congruent triangles?

Given: Rectangle ABCD 
Prove: ∆ABD≅∆CBD 
Given: Rectangle ABCD 
Prove: ∆ABC≅∆ADC

Answer 1

Given: Rectangle ABCD
Prove: ∆ABD≅∆CBD
Solution:

Statement Reason

ABCD is a parallelogram Rectangles are parallelograms since the definition of a parallelogram is a quadrilateral with two pairs of parallel sides.

Segment AD = Segment BC The opposite sides of a parallelogram are Segment AB = Segment CD congruent. This is a theorem about the parallelograms.

∆ABD≅∆CBD SSS postulate: three sides of ΔABD is equal to the three sides of ∆CBD


Given: Rectangle ABCD
Prove: ∆ABC≅∆ADC
Solution:

Statement Reason

Angle A and Angle C Definition of a rectangle: A quadrilateral
are right angles with four right angles.

Angle A = Angle C Since both are right angles, they are congruent

Segment AB = Segment DC The opposite sides of a parallelogram are Segment AD = Segment BC congruent. This is a theorem about the parallelograms.

∆ABC≅∆ADC SAS postulate: two sides and included angle of ΔABC is congruent to the two sides and included angle of ∆CBD