answer for Which of the following transformations would result in two congruent triangles? A vertex x should be moved up 5 units B vertex x should be moved down 10 units C vertex y should be moved left 4 units D vertex z should be moved left 4 units

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answer for Which of the following transformations would result in two congruent triangles? A vertex x should be moved up 5 units B vertex x should be moved down 10 units C vertex y should be moved left 4 units D vertex z should be moved left 4 units

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MrRoyal MrRoyal · Answer 1 · 2025-04-08T17:07:14-04:00

Congruent shapes are shapes that have similar and equal side lengths and angles

The transformation that would result in two congruent triangles is: (b) vertex x should be moved down 10 units

From the diagram (see attachment)

The base of both triangles are equal i.e. YZ = 4 units
The first triangle has a height of 7 units
Triangle XYZ has a height of 3 units

So, the transformation that makes both triangles to be congruent must be applied to the vertex X

Vertex X must either be moved up or down

The number of units (k) up is:

[tex]\mathbf{Height\ of\ XYZ + k = Height\ of\ first\ triangle}[/tex]

So, we have:

[tex]\mathbf{3 + k = 7}[/tex]

Collect like terms

[tex]\mathbf{k = 7 - 3}[/tex]

[tex]\mathbf{k = 4}[/tex]

The number of units (k) down is:

[tex]\mathbf{k - Height\ of\ XYZ = Height\ of\ first\ triangle}[/tex]

So, we have:

[tex]\mathbf{k - 3 = 7}[/tex]

Collect like terms

[tex]\mathbf{k = 7 + 3}[/tex]

[tex]\mathbf{k = 10}[/tex]

This means that:

Vertex x should be moved 4 units up or 10 units down

Hence, the true statement is: (b) vertex x should be moved down 10 units