Which pairs of quadrilaterals can be shown to be congruent using rigid motions? Select all of the sets which can be shown congruent.

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1 Answer
Shwetank Mauria
Nov 28, 2016

#Q1#, #Q2# and #Q3# are all congruent.

Explanation:

As quadrilaterals are drawn on a Cartesian graph, it is easy to see that

#Quadrilateral-1#, #Quadrilateral-2# and #Quadrilateral-3# are all congruent, while #Quadrilateral-4# is different.

The sides of #Quadrilateral-1#, #Quadrilateral-2# and #Quadrilateral-3# can be found using Pythagoras theorem and are #{2,2,sqrt10,sqrt2}# units. Even corresponding angles as well as diagonals two are congruent in these three quadrilaterals.

Naming them as #Q1#, #Q2#, #Q3# and #Q4# respectively, we can say that

pair wise #Q1-=Q2#, #Q2-=Q3# and #Q1-=Q3#.

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