Question

day 3
decide whether the congruence statement is true. explain your reasoning.
$\triangle wxy\cong\triangle yzw$
day 4
decide whether the congruence statement is true.
explain your reasoning. $\triangle abc\cong\triangle cde$
day 5

Explanation:

Day 3

To check if \(\triangle WXY\cong\triangle YZW\), we use the SSS (Side - Side - Side) congruence criterion. In \(\triangle WXY\) and \(\triangle YZW\), \(WX = YZ\) (marked with one tick), \(XY=ZW\) (marked with one tick), and \(WY = WY\) (common side). By SSS, \(\triangle WXY\cong\triangle YZW\).

For \(\triangle ABC\) and \(\triangle CDE\), in \(\triangle ABC\), we have a right - angle at \(C\). In \(\triangle CDE\), we assume the right - angle is not in the same orientation as per the given figure. Also, if we check the side lengths: \(AC\) (marked with one tick) and \(CD\) (marked with one tick) are equal, but \(AB\) (marked with two ticks) and \(CE\) (marked with one tick) are not equal in the proportion required for congruence. Using the right - triangle congruence criteria (HL for right - triangles: hypotenuse - leg), the hypotenuse and legs do not match.

Answer:

The congruence statement \(\triangle WXY\cong\triangle YZW\) is True.

Day 4