IXL - SSS Theorem in the coordinate plane (Geometry practice)

Are

△

and

△

congruent?

yes

ref_doc_title.

Learn with an example

question

Are

△

and

△

congruent?

yes

key idea

The SSS Theorem states that two triangles are congruent if and only if the three sides of one triangle are congruent to the three corresponding sides of the other triangle.

△

≅

△

solution

To see that

△

and

△

are not congruent, calculate the three side lengths of each triangle.

△

has vertices

(

)

(

–

)

and

(

–

)

and

△

has vertices

(

–

)

(

–

)

and

(

–

)

Step 1: Find the side lengths of

△

First, find RT. Since

(

)

and

(

–

)

have the same

-coordinate,

RT is the absolute value of the difference in the

-coordinates.

So,

–

Second, find ST. Since

(

–

)

and

(

–

)

have the same

-coordinate,

ST is the absolute value of the difference in the

-coordinates.

So,

–

Third, find RS. Since

(

)

and

(

–

)

do not have equal

-coordinates

or equal

-coordinates,

use the distance formula to calculate RS. Plug in

(

)

for

(

)

and

(

–

)

for

(

)

and simplify.

Distance formula

(

–

)

(

–

)

Distance formula

Plug in

–

and

(

–

)

(

–

)

Plug in

–

and

Subtract

(

–

)

(

–

)

Subtract

Square

121

Square

Add

202

Add

The three side lengths of

△

are

and

202

Step 2: Find the side lengths of

△

First, find DF. Since

(

–

)

and

(

–

)

have the same

-coordinate,

DF is the absolute value of the difference in the

-coordinates.

So,

–

Second, find EF. Since

(

–

)

and

(

–

)

have the same

-coordinate,

EF is the absolute value of the difference in the

-coordinates.

So,

–

Since no side of

△

has length 12,

is not congruent to

Therefore,

△

is not congruent to

△

by the SSS Theorem.

Looking for more? Try these:

Lesson: Distance formula

Lesson: Congruence

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Work it out

Not feeling ready yet? These can help:

B.13Distance formula

L.2SSS and SAS Theorems

Lesson: Distance formula

Lesson: Congruence

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