# 5.06 Coordinate methods and triangle congruence

## Interactive practice questions

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

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 $\triangle YXZ$YXZ.

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 $\triangle ABC$ABC.

E

$Y$Y does not translate to any vertex of $\triangle ABC$ABC.

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 $\triangle ABC$ABC.

E

$Y$Y does not translate to any vertex of $\triangle ABC$ABC.

F
c

Are $\triangle ABC$ABC and $\triangle YXZ$YXZ congruent?

Yes

A

No

B

Yes

A

No

B
Easy
Approx 2 minutes

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

In the diagram below, $X$X is a translation of $C$C, and $Y$Y is a translation of $A$A.

Move the point $Z$Z so that the resulting triangle $\triangle YZX$YZX is congruent to $\triangle ABC$ABC.

Consider the two triangles drawn in the diagram below.

Are the triangles $\triangle YBC$YBC and $\triangle YXZ$YXZ congruent?

### Outcomes

#### GEO-G.GPE.4

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