5.3 and 5.5 SSS in the Coordinate Plane KEY

University:
California State University, Northridge
Course:
CHEM 100 | Principles of Chemistry
Academic year:

2024
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0

Pages:

1
Author:

Kayla Manseur

5.8 Using SSS in the Coordinate Plane Given the coordinates, determine whether ∆PQR and ∆XYZ are congruent. 1. ∆PQR: P(5, -4), Q(-3, 7), R(0, 2) ∆XYZ: X(-2, -1), Y(9, 7), Z(3, 2) PQ = √[(9 - (-2))^2 + (7 - (-1))^2] = √185 QR = √[(0 - (-3))^2 + (2 - 7)^2] = √34 PR = √[(0 - 5)^2 + (2 - (-4))^2] = √61 XY = √[(-2 - 9)^2 + (-1 - 7)^2] = √185 YZ = √[(3 - 9)^2 + (2 - 7)^2] = √61 XZ = √[(3 - (-2))^2 + (2 - (-1))^2] = √34 Are the triangles congruent? If yes, explain your reasoning and write a congruency statement. ∆PQR ≅ ∆XYZ by SSS 2. ∆PQR: P(-7, -1), Q(4, 9), R(-2, -5) ∆XYZ: X(-11, 4), Y(0, -6), Z(-1, 3) PQ = √[(4 - (-7))^2 + (9 - (-1))^2] = √221 QR = √[(-2 - 4)^2 + (-5 - 9)^2] = √232 PR = √[(-2 - (-7))^2 + (-5 - (-1))^2] = √41 XY = √[(0 - (-11))^2 + (-6 - 4)^2] = √221 YZ = √[(-1 - 0)^2 + (3 - (-6))^2] = √82 XZ = √[(-1 - (-11))^2 + (3 - 4)^2] = √101 Are the triangles congruent? If yes, explain your reasoning and write a congruency statement. These triangles are not congruent (at least by SSS) because there are not 3 pairs of congruent sides.