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Which pairs of triangles can be shown to be congruent using rigid
motions?
Select Congruent or Not congruent for each pair of triangles.
A ABC and A UVW
A ABC and A GHJ
A PQR and A UVW
AGHJ and A PQR
Congruent
O
Not congruent
O
O
O
6+
5+
4
3+
2+
1+
Lo
-7-6-5-4-3-2-1₁ 1
3+
-4+
-5+
-6+
W
7+
G
A
2
3
4
5 6
H
B
7
X

Which pairs of triangles can be shown to be congruent using rigid motions Select Congruent or Not congruent for each pair of triangles A ABC and A UVW A ABC and class=

Respuesta :

sqdancefan

Answer:

  • Congruent: A, C
  • Not congruent: B, D

Step-by-step explanation:

You want to identify the pairs of triangles that are congruent.

Triangles

Triangles ABC, PQR, and UVW are isosceles triangles with a base length of 3√2 and side lengths of √17.

Triangle GHJ is an isosceles triangle with a base length of 4 and side lengths of √13. It is not congruent to any other triangle in the figure.

Hence, we have ...

 ∆ABC & ∆UVW — congruent

  ∆ABC & ∆GHJ — not congruent

  ∆PQR & ∆UVW — congruent

  ∆GHJ & ∆PQR — not congruent

__

Additional comment

The lengths of the sides can be found using the distance formula. Each side length is the square root of the sum of the squares of the lengths of the sides of the rectangle of which it is the diagonal. The long sides of the congruent triangles all fit in a rectangle that is 1×4, so their length is √(1²+4²) = √17. The short sides of ∆GHJ fit in a 2×3 rectangle, so their length is √(2²+3²) = √13.

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