Question

are δvwx and δefg congruent?
yes \t\t no

Explanation:

Step1: Identify Coordinates

Find coordinates of vertices:

• \( \triangle VWX \): \( V(7, -7) \), \( W(8, 8) \), \( X(1, 0) \)
• \( \triangle EFG \): \( E(-8, -9) \), \( F(-1, 5) \), \( G(-10, 1) \)

Step2: Calculate Side Lengths (Distance Formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \))

• For \( \triangle VWX \):

\( VW \): \( \sqrt{(8 - 7)^2 + (8 - (-7))^2} = \sqrt{1 + 225} = \sqrt{226} \)
\( WX \): \( \sqrt{(1 - 8)^2 + (0 - 8)^2} = \sqrt{49 + 64} = \sqrt{113} \)
\( XV \): \( \sqrt{(7 - 1)^2 + (-7 - 0)^2} = \sqrt{36 + 49} = \sqrt{85} \)

• For \( \triangle EFG \):

\( EF \): \( \sqrt{(-1 - (-8))^2 + (5 - (-9))^2} = \sqrt{49 + 196} = \sqrt{245} \)
\( FG \): \( \sqrt{(-10 - (-1))^2 + (1 - 5)^2} = \sqrt{81 + 16} = \sqrt{97} \)
\( GE \): \( \sqrt{(-8 - (-10))^2 + (-9 - 1)^2} = \sqrt{4 + 100} = \sqrt{104} \)

Step3: Compare Side Lengths

No two sides (one from each triangle) have equal lengths. Thus, triangles are not congruent.

Answer:

no