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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

5. Proving Triangle Congruence by SSS

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Exercise 26 Page 624

Using the given coordinates, calculate the length of the triangle's three sides.

No, they are not congruent.

Practice makes perfect

Let's start by drawing the two triangles on a coordinate plane.

According to the Side-Side-Side Congruence Theorem, if three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. To compare them, we should find their lengths. We can do this using the Distance Formula.

Side	Points	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
AB	( -2,1),( 3,-3)	sqrt(( 3-( - 2))^2+( -3- 1)^2)	sqrt(41)
BC	( 3,-3),( 7,5)	sqrt(( 7- 3)^2+( 5-( -3))^2)	sqrt(80)
AC	( -2,1),( 7,5)	sqrt(( 7-( - 2))^2+( 5- 1)^2)	sqrt(97)
DE	( 3,6),( 8,2)	sqrt(( 8- 3)^2+( 2- 6)^2)	sqrt(41)
EF	( 8,2),( 10,11)	sqrt(( 10- 8)^2+( 11- 2)^2)	sqrt(85)
DF	( 3,6),( 10,11)	sqrt(( 10- 3)^2+( 11- 6)^2)	sqrt(74)

We found that only AB and DE are congruent. All the other sides have different lengths. Therefore, the figures are not congruent.

Subchapter links

Communicate Your Answer p.617

Monitoring Progress p.619-621

Exercises p.622-624