Topics
11. Connecting Algebra & Geometry Through Coordinates
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United States of AmericaVirginia
Geometry

11.05 Similarity and congruence in the coordinate plane

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

Consider the two triangles drawn in the diagram below.

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

Loading Graph...
Two triangles are graphed on a Coordinate Plane with axes labeled from 0 to 10. The two triangles shares a common vertex, $Y$Y, at $\left(9,2\right)$(9,2). The vertices of triangle $YBC$YBC are $Y$Y at $\left(9,2\right)$(9,2), $B$B at $\left(6,9\right)$(6,9), and $C$C at $\left(2,4\right)$(2,4). The vertices of triangle $YXZ$YXZ are $X$X at $\left(3,4\right)$(3,4), $Y$Y at $\left(9,2\right)$(9,2), and $Z$Z at $\left(6,10\right)$(6,10). The coordinates are not explicitly labeled.

Yes

A

No

B
Easy
< 1min

Consider the two triangles drawn in the diagram below.

Easy
< 1min

Consider the two triangles drawn in the diagram below.

Easy
< 1min

$\triangle ABC$△ABC has vertices $A$A$\left(1,1\right)$(1,1), $B$B$\left(5,5\right)$(5,5), and $C$C$\left(1,4\right)$(1,4), and $\triangle DEF$△DEF has vertices $D$D$\left(3,3\right)$(3,3), $E$E$\left(7,7\right)$(7,7), and $F$F$\left(3,6\right)$(3,6).

Jimmy wants to determine if the two triangles are similar and calculates the slopes of the sides as follows:

Easy
< 1min
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Outcomes

G.TR.2

The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles.

G.TR.2c

Use coordinate methods, such as the slope formula and the distance formula, to prove two triangles are congruent.

G.TR.3

The student will, given information in the form of a figure or statement, prove and justify two triangles are similar using direct and indirect proofs, and solve problems, including those in context, involving measured attributes of similar triangles.

G.TR.3c

Use coordinate methods, such as the slope formula and the distance formula, to prove two triangles are similar.

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