McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
2. Congruent Triangles
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Exercise 45 Page 352

Look for the side corresponding to HJ in triangle △ ABC.

5

Practice makes perfect
We are given that triangles △ ABC and △ HIJ are congruent. The order of letters in this congruence indicate corresponding vertices. Let's use colors to indicate this correspondence. △ A B C≅△ H I J The question asks for the measure of H J. The side in triangle △ A B C corresponding to H J is A C.

Since corresponding sides in congruent triangles have the same measure, we can find the measure of H J by finding the measure of A C first.

Finding AC

Since the coordinates of A and C are given, we can find the distance of these points using the Distance Formula.
AC=sqrt((x_C-x_A)^2+(y_C-y_A)^2)
AC=sqrt(( 2-( - 1))^2+( - 2- 2)^2)
Simplify right-hand side
AC=sqrt((2+1)^2+(-2-2)^2)
AC=sqrt(3^2+(-4)^2)
AC=sqrt(9+16)
AC=sqrt(25)
AC=5

Finding HJ

Since H J and A C are corresponding sides in congruent triangles △ A B C and △ H I J, their measure is the same. H J= A C=5 The measure of H J is 5.