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

Answer:

Given all the blanks true explained below.

Step-by-step 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

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

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

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

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

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=$\sqrt{3^{2}+2^{2}}=\sqrt{13} units$

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