Question

1. (image of triangles)\\(\text{(a)} \\) triangles \\(abc\\) and \\(dcb\\) are congruent by the angle - angle triangle congruence theorem\\(\text{(b)} \\) triangles \\(abc\\) and \\(dcb\\) are congruent by the angle - side - angle triangle congruence theorem\\(\text{(c)} \\) triangles \\(abc\\) and \\(dcb\\) are congruent by the side - side - side triangle congruence theorem\\(\text{(d)} \\) triangles \\(bac\\) and \\(cdb\\) are congruent by the side - angle - side triangle congruence theorem\\(\text{(e)} \\) triangles \\(abc\\) and \\(dcb\\) are congruent by the side - side - side triangle congruence theorem\\(\text{(f)} \\) there is not enough information to determine if the triangles are congruent.\\15. point \\(m\\) undergoes a reflection over the \\(x\\)-axis. given \\(m(5, - 7)\\), determine \\(m\\).\\(\text{(a)} \\ (5, 7)\\(\text{(b)} \\ (-5, - 7)\\(\text{(c)} \\ (-5, 7)\\(\text{(d)} \\ (-7, 5)\\

Explanation:

Question 15 (Reflection over x - axis)

Step 1: Recall the rule for reflection over x - axis

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. Mathematically, if we have a point \(M(x,y)\), after reflection over the \(x\) - axis, the image \(M'\) has coordinates \((x, - y)\).

Step 2: Apply the rule to the given point

We are given the point \(M(5,-7)\). Here, \(x = 5\) and \(y=-7\). Using the reflection rule over the \(x\) - axis, the \(x\) - coordinate of \(M'\) will be \(5\) (same as the \(x\) - coordinate of \(M\)) and the \(y\) - coordinate of \(M'\) will be \(-(-7)=7\). So, the coordinates of \(M'\) are \((5,7)\).

Answer:

A. \((5, 7)\)

(Note: For the triangle congruence question, the text is a bit unclear due to possible OCR errors. If you can provide a clearer version of the triangle - related question (like the diagram details, clear labels of triangles and their corresponding parts), I can help you solve it as well.)