5. Triangles & Congruence

We wish to determine if the pair of triangles on the coordinate plane below are congruent.

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a

What translations move the point $X$`X` to the point $B$`B`?

Translate $\editable{}$ units left and $\editable{}$ units down.

b

Apply the translation from part (a) to the other two points of the triangle $\triangle YXZ$△`Y``X``Z`.

Which **two** options represent the results?

$Z$`Z` translates to C

A

$Y$`Y` translates to A

B

$Z$`Z` translates to A

C

$Y$`Y` translates to C

D

$Z$`Z` does not translate to any vertex of $\triangle ABC$△`A``B``C`.

E

$Y$`Y` does not translate to any vertex of $\triangle ABC$△`A``B``C`.

F

$Z$`Z` translates to C

A

$Y$`Y` translates to A

B

$Z$`Z` translates to A

C

$Y$`Y` translates to C

D

$Z$`Z` does not translate to any vertex of $\triangle ABC$△`A``B``C`.

E

$Y$`Y` does not translate to any vertex of $\triangle ABC$△`A``B``C`.

F

c

Are $\triangle ABC$△`A``B``C` and $\triangle YXZ$△`Y``X``Z` congruent?

Yes

A

No

B

Yes

A

No

B

Easy

Approx 2 minutes

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On the coordinate plane, algebraically prove geometric theorems and properties.