Question

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Answer 1

For 9, the missing information is whether the hypotenuse of the 2 triangles are equal. The statement would be \(\triangle BAC \cong \triangle DFE \) (HL)

HL congruence refers to the situation where the hypotenuse and a leg of both triangles are equal. There must exist a right angle in both triangles for this to work.

For 10, assuming LNP is a straight line, the missing information is whether MN = NO. The statement would be \(\triangle LNM \cong \triangle PNO \) (SAS)

SAS congruence refers to the situation where a pair of corresponding sides and the included angle are equal. In this case, we know that angle LNM = angle ONP (vert. oppo. angles, assuming LNP is a straight line) and LN = NP. What we're missing is whether MN = NO.

Here's a really great website for your reference: http://www.mathopenref.com/congruenttriangles.html

Answer 2

Whether the hypotenuse of the 2 triangles are equal. (i.e DE and CB)