1. proving congruncy

i cant prove part(b). i think since ABCD is rectangle and not square, Ab is not equal to BC. this means the two triangle cannot be the same.pls help me thanks

2. Originally Posted by helloying
i cant prove part(b). i think since ABCD is rectangle and not square, Ab is not equal to BC. this means the two triangle cannot be the same.pls help me thanks

take the two triangles ABC and the triangle PBQ we have

AB = PB cuz ABP equilateral triangle
BC = BQ cuz BCQ equilateral triangle and
<ABC = < PBQ = 90

the two triangles congruent with SAS side-angle-side in the result you have
AC=PQ

3. Originally Posted by helloying
i cant prove part(b). i think since ABCD is rectangle and not square, Ab is not equal to BC. this means the two triangle cannot be the same.pls help me thanks
A rectangle may be square; it may have equal sides.
A square can ONLY have equal sides.

A square is included in the definition of rectangle.

4. draw AC and PQ
angle ABC = angle PBQ = 90
AB = CB
PB = QB
hence triangle ABC congruent PBQ (SAS)
hence AC = PQ

5. Originally Posted by ukorov
draw AC and PQ
angle ABC = angle PBQ = 90
AB = CB
PB = QB
hence triangle ABC congruent PBQ (SAS)
hence AC = PQ
sorry...mistake:
AB = PB
CB = QB