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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Isosceles and Equilateral Triangles

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Exercise 58 Page 382

Calculate the lengths of the sides of the triangles using the Distance Formula.

No, see solution.

Practice makes perfect

To see whether △ STU and △ XYZ are congruent or not, let's find the lengths of the sides.

Since we know the coordinates of the vertices, we can use the Distance Formula. Let's start with finding ST.

ST=sqrt((x_T-x_S)^2+(y_T-y_S)^2)

SubstitutePoints

Substitute ( 2,2) & ( 4,6)

ST=sqrt(( 4- 2)^2+( 6- 2)^2)

▼

Simplify right-hand side

Subtract terms

ST=sqrt(2^2+4^2)

Calculate power

ST=sqrt(4+16)

Add terms

ST=sqrt(20)

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

Corresponding Sides	Distance Formula	Result
ST and XY	sqrt((4-2)^2+(6-2)^2) ? = sqrt((- 4-(- 2))^2+(6-(- 2))^2)	sqrt(20)≠ sqrt(68)
TU and YZ	sqrt((3-4)^2+(1-6)^2) ? = sqrt((- 3-(-4))^2+(1-6)^2)	sqrt(26) = sqrt(26)
US and ZX	sqrt((2-3)^2+(2-1)^2) ? = sqrt((- 2-(- 3))^2+(- 2-1)^2)	sqrt(2)≠ sqrt(10)

Since not all of the side lengths of △ STU match all of the side lengths of △ XYZ, the triangles are not congruent. △ STU ≆△ XYZ

Subchapter links

Exercises p.378-382