Question

Can anyone check for mistakes please!! Thanks :)

Which pairs of triangles can be shown to be congruent using rigid motions?

Select Congruent or Not Congruent for each pair of triangles.

Answer 1

Nope, no mistakes as far as I can tell! Great job!

Answer 2

Given all the blanks true explained below.

Explanation:

Given the pairs of triangle,

First pair, ΔABC and ΔUVW

In these triangles to prove triangles congruent we need all three sides equal but AB≠UV. Hence, not congruent

Second pair, ΔABC and ΔGHJ

To prove triangles congruent we need all three sides equal but AB≠GH Hence, not congruent

Third pair, ΔABC and ΔPQR

To prove triangles congruent we need all three sides equal

AB=PQ=2 units

`BC=\sqrt{(-1+4)^(2) + (1-4)^(2) } =√(18)units`

`QR=\sqrt{(-1-2)^(2) + (-1+4)^(2) } =√(18)units`

`AC=\sqrt{(-1+4)^(2) + (1-2)^(2) } =√(10)units`

`PR=\sqrt{(-1-2)^(2) + (-1+2)^(2) } =√(10)units`

Hence, BC=QR, AC=PR

All 3 sides equal. By SSS rule both triangles congruent.

Fourth pair, ΔGHJ and ΔUVW

GH=UV=3 units

HJ=VW=2 units

Hence, by Pythagoras theorem,

GJ=UW=
`\sqrt{3^(2)+2^(2)}=√(13) units`

Hence, All 3 sides equal. By SSS rule both triangles congruent.

Fifth pair, ΔGHJ and ΔPQR

To prove triangles congruent we need all three sides equal but PQ≠GH Hence, not congruent

Sixth pair, ΔPQR and ΔUVW

To prove triangles congruent we need all three sides equal but PQ≠UV. Hence, not congruent