Which of these triangle pairs can be mapped to each other using two reflections? Triangles X Y Z and P Y T are connected at point Y. Triangle X Y Z is reflected across X Y and then is reflected another time across Y Z to form triangle P Y T. Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected 3 times to form triangle A Y T. Triangles X Y Z and A Y T are connected at point Y. Triangle X Y Z is reflected across side X Y and then is shifted down to form triangle A Y T. Triangles X Y Z and A Z T are connected at point Z. Triangle X Y Z is reflected and then rotated to form triangle A Z T.

The correct option is  (A). and are connected at point Y. is reflected across XY and then is reflected another time across YZ to form .

Given, and are connected at point Y.

is reflected about XY will shift the marked angle from left to right while the right side angle will remain at the same location and the triangle will remain upright to give

Reflection about the YZ will give the marked angle and the right angle in the same location and the vertex X will then be changed to P.

Thus , can be mapped to with two reflections.

In the second option, we have is reflected 3 times which is more than 2 times as said in question. so this statement is false.

In next option is reflected across side XY and then is shifted downwards to form . since here we have only one reflection, so this statement is also false.

4) In option 4 is reflected and then rotated thus option 4 is also not a correct option.

Hence the correct statement is and are connected at point Y. is reflected across XY and then is reflected another time across YZ to form .

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The correct option is the first option;

Triangle XYZ and PYT are connected at point Y. Triangle XYZ is reflected across XY and then is reflected another time across YZ to form triangle PYT

Step-by-step explanation:

To answer the question we look at each option as follows;

1) The parameters given are triangle XYZ and PYT are connected at point Y

Triangle XY is reflected about XY will shift the marked angle from left to right while the right angle will remain at the same location and the triangle will remain upright to give triangle X'Y'Z'

Reflection about the YZ will give; the marked angle and the right angle in the same location and the vertex X will then be changed to P

Therefore, triangle XYZ can be mapped to triangle PYT with two reflections

2)  In the second option, we have triangle XYZ is reflected 3 times which is more than 2 times as in the question, therefore, option two is less suited as an answer to the question

3) Triangle XYZ is reflected across side XY and then is shifted down to form triangle AYT

Therefore, since we have only one reflection, option 3 is also not appropriate as an answer

4) In option 4 triangle XYZ is reflected and then rotated therefore option 4 is also not a correct option.