topic badge
United States of AmericaPA
High School Core Standards - Geometry Assessment Anchors

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.

Loading Graph...

Two triangles are plotted on the grid. The axes marked from 0 to 10. The vertices for the first triangle are $Y$Y$Z$Z, and $X$X. The first triangle is delineated by vertices $X$X at $\left(7,10\right)$(7,10), $Y$Y at $\left(3,3\right)$(3,3), and $Z$Z at $\left(10,8\right)$(10,8). The vertices for the second triangle are $B$B$A$A, and $C$C. The second triangle is outlined by vertices $A$A at $\left(0,0\right)$(0,0), $B$B at $\left(4,7\right)$(4,7), and $C$C at $\left(7,5\right)$(7,5)$B$B corresponds with $X$X$A$A corresponds with $Y$Y$C$C corresponds with $Z$Z. The coordinates are not explicitly labeled.
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
c

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

Yes

A

No

B
Easy
1min

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

Easy
1min

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.

Easy
1min

Consider the two triangles drawn in the diagram below.

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

Easy
< 1min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

CC.2.3.HS.A.11

Apply coordinate geometry to prove simple geometric theorems algebraically.

What is Mathspace

About Mathspace