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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

7. Scale Drawings and Models

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Exercise 43 Page 605

Calculate the length of the sides of the triangles.

Yes, see solution.

Practice makes perfect

To determine whether the triangles △ JKL and △ XYZ are congruent or not, let's find the length of the sides.

Since we know the coordinates of the vertices, we can use the Distance Formula to find the length of the sides. Let's start with finding JK.

JK=sqrt((x_K-x_J)^2+(y_K-y_J)^2)

SubstitutePoints

Substitute ( 3,9) & ( 4,6)

JK=sqrt(( 4- 3)^2+( 6- 9)^2)

▼

Simplify right-hand side

Subtract terms

JK=sqrt(1^2+(-3)^2)

Calculate power

JK=sqrt(1+9)

Add terms

JK=sqrt(10)

We can find the length of the other sides similarly. Before we find the lengths, notice that the exercise asks about the congruence in a specific order. △ JKL? ≅△ XYZ This means that we need to check the lengths between the corresponding sides to see if each segment is congruent.

Corresponding Segments	Lengths	Congruent?
JK XY	sqrt((4-3)^2+(6-9)^2)=sqrt(10) sqrt((2-1)^2+(4-7)^2)=sqrt(10)	Yes ✓
KL YZ	sqrt((1-4)^2+(5-6)^2)=sqrt(10) sqrt((-1-2)^2+(3-4)^2)=sqrt(10)	Yes ✓
JL XZ	sqrt((1-3)^2+(5-9)^2)=2sqrt(5) sqrt((-1-1)^2+(3-7)^2)=2sqrt(5)	Yes ✓

Since all three side pairs are congruent, the Side-Side-Side (SSS) Congruence Postulate guarantees that the triangles are congruent. △ JKL≅△ XYZ

Subchapter links

Exercises p.602-605