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
